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>> Hello, and I'm glad you've joined us for the Cypress College Math Review

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on percent applications.

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Objective one: Percent
equation: 30 is half of 60

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and another way to
say half is 50%.

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So 30 is 50% of 60.

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We want to translate this
into a mathematical equation.

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The word is is our verb.

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That's where the
equal sign goes.

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Of in mathematics
is multiplication.

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So 30 equals 50% times 60.

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Recall that several
percentages are easier

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to work with as fractions.

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Here's some examples: 10% is
the same thing as one-tenth;

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20% is one-fifth; 25% is
the same at one-fourth,

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33-1/3% is one-third, but we
often just approximate 33%

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for one-third; 50% is one-half;
67% is a common approximation

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for two-thirds, 75% is
three-fourths, and 100% is one.

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Example: What's 75% of 400?

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What, we'll call that
x, is, so equals,

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75% of, so multiply, 400.

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Now we have an equation.

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Seventy-five percent
is the same as 0.75.

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We could multiply by 0.75,
but isn't there an easier way?

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Seventy-five percent of
something is the same thing

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as three-quarters of that thing.

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So we can multiply
by either 0.75

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or three-quarters,
whichever is easier.

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Use the form of a number,
fraction or decimal,

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that's easiest for you.

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Let's use three-quarters
this time.

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Our equation becomes x equals
three-quarters times 400.

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We can cancel four out of
four, which gives us one,

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four out of 400 gives us 100.

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So now we have three
times 100, which is 300.

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Therefore, 300 is 75% of 400.

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Seventy is 40% of what?

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Let's translate that into
a mathematical equation.

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Seventy is, so equals,
40% of, means times, what,

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well there we'll
put our variable,

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x. So 70 equals 40% times x.
Let's write 40% as a decimal.

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That's probably easier

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than using the fractional
form for this one.

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As a decimal 40% is 0.40.

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So 70 equals 0.40 times
x. We want to solve for x.

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So divide both sides by 0.40,
and we get that x equals 175.

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Hence 70 is 40% of 175.

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Ninety-five is what
percent of 190?

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Translating that
into an equation,

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we get 95 equals x times 190.

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We can rewrite the right
side of our equation as 190x

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since order doesn't
matter in multiplication.

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To solve for x we
divide both sides by 190.

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95 divided by 190 is 0.5.

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Now we change that to
a percent, 0.5 is 50%.

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Our answer is 95 is 50% of 190.

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Let's take another
look at this problem.

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Ninety-five was what
percent of 190?

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Ninety-five is part of 190.

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We could call 95 the part and
190 the whole in the problem.

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So our percent equation
could be written

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as part equals percent of whole.

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The whole is the value that
comes after the word of.

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Pause the video and
try these problems.

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Objective Two: Percent
Proportion.

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One-half equals 50%.

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Percent means out of 100.

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One-half equals 50 out of 100.

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One out of two equals
50 out of 100.

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Well that makes sense.

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If we were to reduce
the fraction 50/100,

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we would get one-half.

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One out of two.

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One is the part of two.

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So one out of two
represents part out of whole,

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50 out of 100 represents
50 percent.

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This gives us our
percent proportion.

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Part out of whole equals
percent out of 100.

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Example: 20% of 75 is what?

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Part is percent of whole.

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Here's our percent proportion,
the verb is separates the part

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from the rest of the pieces.

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The part is unknown.

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Let's call that x.
The percent is 20%.

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The whole comes after
the word of.

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So the whole is 75.

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Our percent proportion would be
x over 75 equals 20 over 100.

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Now to solve, we cross multiply.

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X times 100, that's 100x;
75 times 20 is 1500.

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Now 100 is being multiplied
times x. So we need

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to divide both sides by 100 to
solve for x. Divide both sides

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by 100, 1500 divided
by 100 is 15.

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Hence 15 is 20% of 75.

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Notice that the percent
proportion is just another way

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to do percent problems.

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You can do them using
the percent equation

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or percent proportion.

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Use the method that's
easiest for you

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or for the problem
that you're doing.

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Sixty is 15% of what?

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Here's our percent proportion.

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Part is percent of whole, so our
part is 60; the percent is 15,

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whole then is the unknown.

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We'll call that x. Put
these into our proportion.

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Sixty over x equals 15 over 100,

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part over whole equals
percent over 100.

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Now let's solve the proportion.

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Cross multiply.

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Sixty times 100 is
6000, x times 15 is 15x.

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Now divide both sides by 15,
6000 divided by 15 is 400.

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Hence 60 is 15% of 400.

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Example: Eighty is
what percent of 500?

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Part is percent of
whole, so our part is 80;

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percent is our unknown, we'll
call that x; the whole is 500.

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Eighty over 500 equals
x over 100.

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Now let's solve it.

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Cross multiply.

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Eighty times 100 is 8000, 500
times x. Now divide both sides

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by 500, 8000 divided
by 500 is 16.

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Therefore 80 is 16% of 500.

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Sixty is twice 30.

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Another way to say that
is 60 is two times 30.

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If we convert 200% into
either decimal or fraction,

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you get the number two.

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So two is equal to 200%.

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We can then rewrite our
sentence as 60 is 200% of 30.

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The part is 60; the percent
is 200%, and the whole is 30.

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In this case, the part
is bigger than the whole.

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The words part and whole
can definitely be confusing.

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The whole is the original,

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what you started with,
or what it is out of.

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There are many cases
where you end up with more

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than what you started with.

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Example: What percent
of 200 is 450.

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Four hundred fifty is our part.

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It's by itself on the
other side of the verb.

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Percent is our unknown,
that's x. The whole comes

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after the word of,
so the whole is 200.

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Since the part is bigger
than the whole, definitely,

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450 is bigger than 200,

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our percent will be
bigger than 100%.

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So we have 450 over
200 equals x over 100.

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Now we solve.

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Cross multiply, 45,000 equals
200x, divide both sides

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by 200 and we get 225.

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Therefore 450 is 225% of 200.

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Pause the video and
try these problems.

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Objective Three:
Percent applications.

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Example: McKenzie has 9% of her
earnings automatically deposited

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into her savings account.

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This way she puts $270 into
her savings account each month.

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What's her monthly earnings?

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Let's use the percent
equation for this problem.

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We should reword the
problem to make it sound

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like part is percent of whole.

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McKenzie's savings are
9% of her earnings.

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So savings are 9% of earnings.

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The savings was the $270.

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So 270 equals 9% of earnings.

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Our unknown is her earnings.

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We'll call that x.
270 equals 9% times x.

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As a decimal, 9% is .09.

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Be sure and move the
decimal place twice.

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270 equals 0.09x.

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To solve, we divide
both sides by .09,

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and when we divide,
we get $3000.

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So McKenzie makes
$3000 per month.

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Ethan had budgeted
$320 for textbooks.

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But he ended up spending $375.

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The amount that he spent was
what percent of his budget?

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Round your answer to the
nearest tenth of a percent.

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Again let's use the
percent equation.

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Let's reword the sentences.

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The amount that he
spent was what percent

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of the budgeted amount?

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$375 is what he spent.

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The percent is our unknown.

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We'll call that x, and
he had budgeted $320.

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So 375 equals 320 times
x. Solve the equation.

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Divide both sides by 320 and
we get approximately 1.171875.

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We need to round our
answer to the nearest tenth

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of a percent, but
don't round yet.

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Change this to a percent first.

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So 1.171875 as a percent
would be 117.1875%.

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I move the decimal place
to the right twice.

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Now we want to round to the
nearest tenth of a percent.

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A tenth of a percent.

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Well the tenth's place
is where this one is,

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so we look next door
to the eight.

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Is that a five or greater?

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Yes. Therefore the
one becomes a two.

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So we rounded up to 117.2%.

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Ethan spent 117.2% of
what he had budgeted.

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Owen earned a score
of 85% on his test.

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There were 80 problems
on the test.

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How many did he get correct?

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For this problem, we'll
use the percent proportion.

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It doesn't matter.

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I just wanted to
show both methods.

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Let's rewrite it.

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The number he got correct
was 85% of the total number

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of problems on the test.

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So the number correct
was 85% of 80.

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Part is the unknown.

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That's our x. Percent is
85 and the whole is 80.

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So x over 80 equals 85 over 100.

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Now we solve it.

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Cross multiply, 100x
equals 6800.

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Divide both sides by 100,
6800 divided by 100 is 68,

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so Owen did 68 problems
correctly on the test.

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A food label indicates
one serving

00:16:27.606 --> 00:16:30.496
of cereal contains 250 calories

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of which 90 calories
are provided by fat.

00:16:35.046 --> 00:16:38.006
What percent fat does
the food source contain?

00:16:38.816 --> 00:16:43.326
This is a little confusing
since the word of appears twice

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and neither time
does it mean multiply

00:16:45.736 --> 00:16:47.326
with the whole coming after it.

00:16:47.906 --> 00:16:49.676
Let's sort this out.

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90 is the fat calories,
250 is the total calories,

00:16:56.056 --> 00:17:00.826
so 250 is the whole
and 90 is the part.

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Percent's the unknown.

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We'll call that x. In
our percent proportion,

00:17:07.616 --> 00:17:11.736
90 over 250 equals x over 100.

00:17:12.596 --> 00:17:13.196
Now we solve.

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Cross multiply, 9000
equals 250x.

00:17:19.536 --> 00:17:21.166
Divide both sides by 250.

00:17:21.906 --> 00:17:23.526
So x is 36.

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The cereal is 36% fat.

00:17:33.676 --> 00:17:37.146
A food label indicates that
each serving will have 80 grams

00:17:37.146 --> 00:17:38.216
of carbohydrates.

00:17:39.316 --> 00:17:43.786
That translates into 320 food
calories or kilocalories.

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If there are a total of 608
kilocalories in each serving,

00:17:49.446 --> 00:17:51.386
what percent is carbohydrates?

00:17:51.926 --> 00:17:58.206
Wait a minute, 80 grams, 320
kilocalories, 608 kilocalories.

00:17:58.256 --> 00:17:59.616
We've got an extra number.

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But 80 grams translates
into 320 kilocalories.

00:18:06.176 --> 00:18:07.736
So we don't use the 80 number.

00:18:08.906 --> 00:18:11.636
We're comparing 320 kilocalories

00:18:11.636 --> 00:18:14.896
of carbohydrates to
608 kilocalories.

00:18:15.086 --> 00:18:15.816
That's the total.

00:18:16.486 --> 00:18:18.066
Let's rewrite it.

00:18:18.616 --> 00:18:23.616
Kilocalories of carbohydrates
equals what percent

00:18:24.326 --> 00:18:26.656
of total kilocalories?

00:18:27.186 --> 00:18:33.056
As an equation, that would
be 320 equals x times 608.

00:18:35.016 --> 00:18:37.556
320 equals 608x.

00:18:38.906 --> 00:18:44.206
Divide both sides by 608
to solve, and we get 0.525.

00:18:45.166 --> 00:18:47.346
We want to change
that to a percent,

00:18:47.546 --> 00:18:50.036
so we move the decimal
place to the right twice.

00:18:50.966 --> 00:18:53.726
So as a percent, that's 52.5%.

00:18:54.706 --> 00:18:57.976
Therefore the food is
52.5% carbohydrates.

00:19:04.106 --> 00:19:04.976
Pause the video and
try these problems.

00:19:17.386 --> 00:19:20.866
Objective Four: Calculating
tax and discounts.

00:19:21.576 --> 00:19:24.616
Let's say you want to buy
an item that cost $200.

00:19:25.066 --> 00:19:26.686
The tax rate is 5%.

00:19:27.356 --> 00:19:29.336
How much tax will you pay?

00:19:29.856 --> 00:19:35.336
The tax is our part, and
the tax rate is the percent,

00:19:36.526 --> 00:19:39.536
and the original cost of
the item is our whole,

00:19:40.686 --> 00:19:43.916
part is percent of whole.

00:19:44.446 --> 00:19:50.626
So tax equals tax rate
times the original price.

00:19:51.946 --> 00:19:54.166
That's our formula to find tax.

00:19:55.206 --> 00:20:01.726
For this problem, tax
equals 5% of $200.

00:20:03.226 --> 00:20:05.216
Now we change 5% to a decimal.

00:20:05.216 --> 00:20:06.396
That would be .05.

00:20:07.656 --> 00:20:14.376
Tax equals .05 times 200, and
we multiply, and we get 10.

00:20:15.036 --> 00:20:16.716
So the tax is $10.

00:20:18.356 --> 00:20:21.686
Remember that the tax is not 5%.

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That's the tax rate.

00:20:25.386 --> 00:20:30.526
Unfortunately, in our language,
we commonly call it 5% tax.

00:20:31.616 --> 00:20:34.036
You will see this
all over the place,

00:20:34.566 --> 00:20:38.156
but remember tax is money.

00:20:38.716 --> 00:20:40.116
It is not percent.

00:20:40.946 --> 00:20:47.326
Tax is a percent of a quantity,
not the percent itself.

00:20:48.966 --> 00:20:55.026
If someone tells you that
the tax is 5%, which is .05,

00:20:55.826 --> 00:20:59.156
you will not be paying
five cents tax.

00:21:00.556 --> 00:21:07.226
Tax is 5% of the selling
of the selling price.

00:21:07.226 --> 00:21:09.826
How much would you end
up paying for the item?

00:21:10.416 --> 00:21:15.266
If you take the original
price plus the tax,

00:21:15.736 --> 00:21:17.366
we get the final price.

00:21:17.836 --> 00:21:21.146
For this item, the
original price was $200.

00:21:21.796 --> 00:21:23.506
The tax was $10.

00:21:24.036 --> 00:21:28.626
$200 plus $10 is $210.

00:21:29.246 --> 00:21:31.966
So you would pay
$210 for the item.

00:21:39.076 --> 00:21:43.536
Robin bought a printer
priced at $267.95.

00:21:44.476 --> 00:21:47.666
The sales tax rate was 7.5%.

00:21:48.686 --> 00:21:50.716
How much did she
pay for the printer?

00:21:52.316 --> 00:21:56.866
The original price plus the
tax equals the final price.

00:21:58.086 --> 00:21:59.706
Recall that we calculate

00:22:00.066 --> 00:22:04.266
by multiplying the tax rate
times the original price.

00:22:05.136 --> 00:22:09.026
The original price was $267.95.

00:22:09.936 --> 00:22:12.866
The tax rate was 7.5%.

00:22:14.066 --> 00:22:18.206
As a decimal, that
would be 0.075.

00:22:19.416 --> 00:22:20.686
So here's our equation.

00:22:22.146 --> 00:22:25.176
Order of operations
says to multiply first.

00:22:25.776 --> 00:22:28.076
That gives us 20.10.

00:22:29.216 --> 00:22:30.496
This is the tax.

00:22:31.266 --> 00:22:41.576
The original price was
$267.95 and the tax is $20.10.

00:22:41.726 --> 00:22:44.046
We add to get the final price.

00:22:44.506 --> 00:22:48.966
The final price is $288.05.

00:22:54.676 --> 00:22:56.386
Louis purchased 10
pounds of steak.

00:22:57.036 --> 00:22:59.946
His final bill was $73.05.

00:23:00.816 --> 00:23:02.426
Sales tax was 8%.

00:23:03.006 --> 00:23:04.936
What was the original
price of the steak?

00:23:05.876 --> 00:23:06.736
Here's our formula.

00:23:07.396 --> 00:23:11.236
We calculate tax by multiplying
the tax rate times the

00:23:11.236 --> 00:23:12.096
original price.

00:23:12.976 --> 00:23:13.926
What are we given?

00:23:14.446 --> 00:23:17.226
Well his final bill was $73.05.

00:23:17.226 --> 00:23:18.796
So that's the final cost.

00:23:19.726 --> 00:23:21.326
Sales tax was 8%.

00:23:22.436 --> 00:23:24.326
Remember this is
often how we say it

00:23:24.326 --> 00:23:26.036
in our language,
but this is wrong.

00:23:26.326 --> 00:23:28.226
The sales tax rate is 8%.

00:23:29.186 --> 00:23:31.146
Our unknown is the
original price.

00:23:31.146 --> 00:23:35.866
Let's call that x. We have
our equation all set up now.

00:23:36.936 --> 00:23:39.066
What do we do over here
on the left though?

00:23:39.066 --> 00:23:41.956
We have x plus .08x.

00:23:42.866 --> 00:23:43.786
Let's see.

00:23:43.786 --> 00:23:45.646
You can add like terms, right?

00:23:45.676 --> 00:23:48.796
If I have 2x plus 3x,
that would give me 5x.

00:23:48.796 --> 00:23:51.386
So you add the numbers in
front, they're the coefficients.

00:23:52.776 --> 00:23:54.976
So what's in front of this x?

00:23:54.976 --> 00:23:55.626
It's a one.

00:23:56.396 --> 00:23:58.236
So one plus .08.

00:23:58.366 --> 00:24:02.716
So we need to add 1 plus .08.

00:24:03.786 --> 00:24:07.986
Line up the decimal
places and we get 1.08.

00:24:08.766 --> 00:24:13.816
Our equation is 1.08x
equals 73.05.

00:24:15.056 --> 00:24:20.446
Now divide both sides
by 1.08 and we get 67.64

00:24:20.686 --> 00:24:22.366
after we round to
the nearest cent.

00:24:23.556 --> 00:24:28.076
Therefore the original price
of the steak was $67.64.

00:24:28.656 --> 00:24:36.776
If you added 100% and
8%, you would get 108%.

00:24:36.776 --> 00:24:39.556
So here's our percent equation.

00:24:40.526 --> 00:24:42.456
Part is percent of whole.

00:24:43.196 --> 00:24:50.386
The final price equals 108%
of the original price, 108%.

00:24:50.946 --> 00:24:55.356
So the 100% is the
original price and 8%

00:24:55.356 --> 00:24:57.056
of the original price
is the tax.

00:24:57.056 --> 00:25:01.406
So 108% would include the
original price plus the tax.

00:25:02.196 --> 00:25:04.056
We could have started
here instead.

00:25:05.086 --> 00:25:08.876
The final cost was $73.05.

00:25:09.036 --> 00:25:13.106
That equals 108% of
the original price.

00:25:13.706 --> 00:25:17.486
108% is 1.08 as a decimal.

00:25:18.376 --> 00:25:22.056
Divide both sides by 1.08
and we get the same answer.

00:25:22.866 --> 00:25:23.976
It's just another way
to think of the problem.

00:25:30.046 --> 00:25:32.906
Janice bought a dress
for $37.80.

00:25:33.336 --> 00:25:35.776
The dress was on
sale for 20% off.

00:25:36.636 --> 00:25:38.856
What was the original
price before the discount?

00:25:39.636 --> 00:25:43.046
For sales, you take the original
price and subtract the discount

00:25:43.046 --> 00:25:44.246
to get the final cost.

00:25:44.406 --> 00:25:45.456
Makes sense?

00:25:45.616 --> 00:25:46.426
You pay less.

00:25:46.996 --> 00:25:49.786
Just like for tax, to find
the amount of the discount,

00:25:49.786 --> 00:25:53.826
you multiply the discount
rate times the original price.

00:25:53.826 --> 00:25:55.826
So here's our formula.

00:25:56.596 --> 00:25:57.636
What do we know?

00:25:58.326 --> 00:26:00.246
She spent $37.80.

00:26:00.246 --> 00:26:01.696
So that's the final price.

00:26:02.286 --> 00:26:05.206
The discount rate was 20%.

00:26:05.836 --> 00:26:07.956
We don't know the
original price.

00:26:08.036 --> 00:26:14.816
Let's call that x. So original
price, x, discount rate 20%

00:26:14.816 --> 00:26:22.886
or .2, original price x again,
equals final price, 37.8.

00:26:23.936 --> 00:26:26.096
Once again, we need
to combine like terms.

00:26:26.796 --> 00:26:31.476
We have 1x minus 0.2x.

00:26:32.046 --> 00:26:35.376
We need to subtract .2 from one.

00:26:36.346 --> 00:26:39.646
Line up the decimal
places, and we get .8.

00:26:41.186 --> 00:26:45.926
Now we have .8x equals 37.8.

00:26:46.656 --> 00:26:51.866
Divide both sides by
.8 and we get 47.25

00:26:52.066 --> 00:26:54.726
after we round to
the nearest cent.

00:26:54.816 --> 00:26:59.346
Hence the original price
of the dress was $47.25.

00:26:59.916 --> 00:27:02.306
Is there another way that we
could have done this problem?

00:27:03.266 --> 00:27:05.976
Originally, you pay 100%
of a produce of course.

00:27:06.516 --> 00:27:08.666
If it's discounted by 20%,

00:27:09.296 --> 00:27:14.346
that's 100% minus 20%,
that gives you 80%.

00:27:15.216 --> 00:27:18.886
So the final price equals
80% of the original cost.

00:27:19.456 --> 00:27:20.976
That definitely sounds easier.

00:27:21.926 --> 00:27:27.846
Final price 37.8 equals
80% times original price,

00:27:28.086 --> 00:27:33.866
x. 37.8 equals .8
times x and divide

00:27:33.866 --> 00:27:36.296
and we get the same answer.

00:27:37.466 --> 00:27:40.496
Let's say that you've been
asked by your employer to go

00:27:40.496 --> 00:27:43.106
around to all the
price tags in the store

00:27:43.106 --> 00:27:45.446
and reduce the prices by 20%.

00:27:46.836 --> 00:27:50.496
You could go around and
figure out 20% of each price,

00:27:50.496 --> 00:27:52.286
that gives you the discount.

00:27:53.096 --> 00:27:56.106
Then you'd need to subtract that
discount from the original price

00:27:56.106 --> 00:27:57.556
to get the discounted price.

00:27:58.006 --> 00:28:03.796
Or taking away 20% of the
price is the selling it

00:28:03.796 --> 00:28:05.486
for 80% of the price.

00:28:06.456 --> 00:28:11.146
Wouldn't it be quicker to just
multiply each price by .8?

00:28:14.536 --> 00:28:16.436
Noah bought toner
for his printer.

00:28:16.716 --> 00:28:18.776
He paid $29.16.

00:28:19.096 --> 00:28:21.416
The price tag read $27.00.

00:28:21.586 --> 00:28:23.176
What was the sales tax rate?

00:28:24.546 --> 00:28:28.806
Since original price plus
tax equals final price,

00:28:29.116 --> 00:28:32.006
we can subtract the original
price from both sides

00:28:32.006 --> 00:28:34.486
of that equation
and solve for tax.

00:28:35.146 --> 00:28:39.556
So tax equals the final price
minus the original price.

00:28:40.496 --> 00:28:46.816
In our problem, tax
equals $29.16 minus $27.00

00:28:47.256 --> 00:28:49.246
and that's $2.16.

00:28:49.516 --> 00:28:51.736
So the tax was $2.16.

00:28:52.826 --> 00:28:56.216
Now we need to find
the sales tax rate.

00:28:57.036 --> 00:28:59.596
Let's use the percent
proportion this time.

00:29:00.686 --> 00:29:06.906
The part is tax, which is $2.16,
the percent is our unknown,

00:29:07.586 --> 00:29:12.196
and the whole is the
original price, $27.00.

00:29:12.456 --> 00:29:13.806
Always the original.

00:29:14.926 --> 00:29:21.156
So we have 2.16 over
27 equals x over 100.

00:29:22.476 --> 00:29:26.496
Cross multiply, divide
and we get eight.

00:29:27.086 --> 00:29:30.256
The sales tax rate was 8%.

00:29:33.556 --> 00:29:38.196
Yank's hardware store just put
their paint on sale for 15% off.

00:29:39.006 --> 00:29:42.866
If the original price for a
gallon of latex enamel was $35,

00:29:43.236 --> 00:29:44.216
what's the sale price?

00:29:45.346 --> 00:29:48.846
Recall that the original price
minus the discount gives you the

00:29:48.846 --> 00:29:49.646
final cost.

00:29:50.646 --> 00:29:51.986
To calculate the discount,

00:29:52.226 --> 00:29:55.616
we multiply the discount rate
times the original price.

00:29:56.166 --> 00:29:57.126
What do we know?

00:29:57.406 --> 00:29:59.526
We know the original
price was $35

00:29:59.686 --> 00:30:00.976
and we know the discount
rate is 15%.

00:30:01.066 --> 00:30:05.136
We do not know the final price.

00:30:06.266 --> 00:30:07.756
Order of operations tells us

00:30:07.756 --> 00:30:10.376
to multiply first
and then subtract.

00:30:11.656 --> 00:30:15.546
Therefore the sale
price is $29.75.

00:30:21.476 --> 00:30:22.976
Pause the video and
try these problems.

00:30:35.166 --> 00:30:38.126
Objective Five: Percent
increase or decrease.

00:30:38.786 --> 00:30:41.306
We often want to find out
how much something has gone

00:30:41.306 --> 00:30:42.586
up or down.

00:30:43.066 --> 00:30:48.176
In 1970, the average price for
a loaf of bread was 25 cents.

00:30:48.656 --> 00:30:51.906
In 1980, the price was 50 cents.

00:30:52.636 --> 00:30:55.556
In 1990, the price was 70 cents.

00:30:56.466 --> 00:31:02.096
So the price rose by 25
cents between 1970 and 1980.

00:31:02.706 --> 00:31:06.396
And it rose by 20
cents by 1980 and 1990.

00:31:07.226 --> 00:31:08.286
About the same, right?

00:31:08.996 --> 00:31:10.256
Not really.

00:31:11.156 --> 00:31:18.516
The price rose by 100% between
1970 and 1980, but it only went

00:31:18.516 --> 00:31:23.726
up by 40% between 1980 and 1990.

00:31:23.836 --> 00:31:27.196
It's usually more useful to
look at the percent increase

00:31:27.196 --> 00:31:32.036
or decrease and not the
actual increase or decrease.

00:31:33.156 --> 00:31:37.566
To find the percent increase, we
take the amount of the increase

00:31:38.046 --> 00:31:39.776
and divide it by the original.

00:31:40.726 --> 00:31:41.976
Same idea for percent decrease.

00:31:48.046 --> 00:31:50.496
Example: The price
of oatmeal has gone

00:31:50.496 --> 00:31:55.126
up from $4.50 per
box to $6.75 per box.

00:31:55.436 --> 00:31:57.356
Find the percent increase.

00:31:57.966 --> 00:31:59.146
Here's our formula.

00:31:59.756 --> 00:32:02.646
We need to find the amount
of the increase first.

00:32:03.226 --> 00:32:07.466
So we take $6.75
and subtract $4.50.

00:32:07.916 --> 00:32:10.346
That gives us $2.25.

00:32:10.936 --> 00:32:13.856
That's the amount of the
increase or how much the price

00:32:13.856 --> 00:32:15.766
of oatmeal has gone up.

00:32:16.156 --> 00:32:19.036
We divide that by the
original, always the original,

00:32:19.366 --> 00:32:21.506
so that would be $4.50.

00:32:21.976 --> 00:32:24.156
And we get 0.5.

00:32:25.176 --> 00:32:28.186
0.5 as a percent is 50%.

00:32:29.186 --> 00:32:31.976
Therefore the price of
oatmeal went up by 50%.

00:32:38.046 --> 00:32:40.366
Tessie had been paying
$65 a month

00:32:40.366 --> 00:32:41.886
for electricity at
her apartment.

00:32:42.796 --> 00:32:45.426
Now she is more careful
about turning off lights

00:32:45.426 --> 00:32:48.266
and unplugging appliances
that are not being used.

00:32:48.536 --> 00:32:51.516
Her electric bill has
gone down to $50 a month.

00:32:52.286 --> 00:32:54.536
What's the percent
decrease in her bill.

00:32:56.046 --> 00:32:59.826
First we find the amount of the
decrease, so we subtract $50

00:32:59.826 --> 00:33:02.596
from $65, and that's $15.

00:33:03.266 --> 00:33:07.776
To find the percent
decrease, we divide the $15

00:33:08.046 --> 00:33:10.736
by the original, which was $65.

00:33:11.266 --> 00:33:17.446
That gives us approximately
.23 or 23%.

00:33:18.276 --> 00:33:21.956
Tessie electric bill
went down by 23%.

00:33:27.186 --> 00:33:31.306
Kiley and Juanita paid a
total of $65 for their meal.

00:33:32.126 --> 00:33:34.746
Their bill is $54.25.

00:33:35.246 --> 00:33:38.406
What was the tip rate that
they left for the server?

00:33:39.126 --> 00:33:42.766
Well the tip rate is the
same as the percent increase.

00:33:43.436 --> 00:33:45.486
What they paid above
the original.

00:33:46.206 --> 00:33:52.096
The amount of increase we
subtract $65 minus $54.25,

00:33:52.766 --> 00:33:55.456
which is $10.75.

00:33:55.956 --> 00:33:58.076
Now we want to find
the tip rate.

00:33:58.826 --> 00:34:02.556
So we're going to take
the $10.75 and divide it

00:34:02.556 --> 00:34:06.426
by the original,
which was $54.25.

00:34:07.686 --> 00:34:14.046
When we divide and we round, we
get approximately .20 or 20%.

00:34:15.266 --> 00:34:19.466
Kiley and Juanita
left a 20% gratuity.

00:34:25.046 --> 00:34:30.166
Ray made $1,365 on an
investment that he made.

00:34:30.766 --> 00:34:35.026
His broker told him that he
had cleared 15% on his money.

00:34:35.726 --> 00:34:37.216
How much had Ray invested?

00:34:38.406 --> 00:34:39.186
Here's our formula.

00:34:39.736 --> 00:34:41.076
What are we given?

00:34:42.036 --> 00:34:47.336
Well $1,365 is not the original
investment or the amount

00:34:47.336 --> 00:34:48.596
of money he had at the end.

00:34:49.306 --> 00:34:52.686
That's the amount of money
that he made as profit.

00:34:54.186 --> 00:34:56.796
That's the amount
that his money grew.

00:34:57.456 --> 00:34:59.866
So that is the amount
of the increase.

00:35:00.256 --> 00:35:02.386
We're given the amount
of the increase

00:35:02.996 --> 00:35:05.026
and the percent increase.

00:35:06.196 --> 00:35:08.406
We wish to find the
original investment.

00:35:08.996 --> 00:35:13.546
The percent increase
is 15% or .15,

00:35:14.676 --> 00:35:18.706
the amount of increase
is $1,365,

00:35:19.806 --> 00:35:22.276
the original investment
is unknown.

00:35:22.386 --> 00:35:25.666
So we'll call that
x. We have a fraction

00:35:25.666 --> 00:35:27.676
on the right, but
not on the left.

00:35:28.936 --> 00:35:32.506
We can write .15
as .15 over one.

00:35:32.676 --> 00:35:33.816
You can put anything over one.

00:35:34.206 --> 00:35:35.916
That doesn't change it.

00:35:36.176 --> 00:35:39.576
Now we cross multiply,
then we divide.

00:35:40.556 --> 00:35:43.136
So x equals 9100.

00:35:43.936 --> 00:35:46.976
So Ray had invested $9,100.

00:35:53.046 --> 00:35:55.216
Pause the video and
try these problems.