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.