SAT Mc Graw Hill 2011

CHAPTER 7 / ESSENTIAL PRE-ALGEBRA SKILLS 287

Word Problems with Percents

The word percentsimply means divided by 100.

Word problems are easy to solve once you

know how to translate sentences into equa-

tions. Use this key:

Example:

What number is 5 percent of 36?

Use the translation key to translate the question

into

Then simplify to get x= 1.8.

Example:

28 is what percent of 70?

Use the translation key to translate the question

into

Then simplify to get 28 = .7xand divide by .7 to get

x= 40.

To convert a percent into a decimal, just re-

member that percent means divided by 100

and that dividing by 100 just means moving

the decimal two places to the left.

Example:

35.7% = 35.7÷100 = .357 .04% = .04÷100 = .0004

Finding “Percent Change”

Some word problems ask you to find the “per-

cent change” in a quantity, that is, by what per-

cent the quantity increased or decreased. A

percent change is always the percent that the

changeis of the original amount. To solve

these, use the formula

28

100

=× 70

x

x=×

5

100

36

Percent change=

final amount – starting amount

× 100%

starting amount

Example:

If the population of Bradford increased from

30,000 to 40,000, what was the percent increase?

According to the formula, the percent change is

Increasing or Decreasing by Percents

When most people want to leave a 20% tip at a restau-

rant, they do twocalculations: First, they calculate

20% of the bill, and then they add the result to the orig-

inal bill. But there’s a simpler, one-step method: Just

multiply the bill by 1.20! This idea can be enormously

helpful on tough percent problems. Here’s the idea:

When increasing or decreasing a quantity by a

given percent, use the one-step shortcut: Just

multiply the quantity by the final percentage.

For instance, if you decrease a quantity by

10%, your final percentage is 100% – 10% =

90%, so just multiply by 0.9. If you increase a

quantity by 10%, your final percentage is 100% +

10% = 110%, so just multiply by 1.1.

Example:

If the price of a shirt is $60 but there is a 20% off

sale and a 6% tax, what is the final price?

Just multiply $60 by .80 and by 1.06: $60 .80 

1.06 = $50.88

Here’s a cool fact that simplifies some percent

problems: a% of b is always equal to b% of a.

So, for instance, if you can’t find 36% of 25 in

your head, just remember that it’s equal to

25% of 36! That means 1/4 of 36, which is 9.

40 000 30 000

30 000

100 33

1

3

,,

,

%%

−

×=

Lesson 5: Percents

percent means ÷ 100

is means =

of means ×

what means x, y, n,etc.