Basic Mathematics for College Students

522 Chapter 6 Percent

Self Check 2

What number is 36% of 400?

Now TryProblems 19 and 71







The Language of Mathematics When we find the value of the variable that

makes a percent proportion true, we say that we have solved the proportion.

In Example 2, we solved 500 x  10084 to find that the variable xis 420.

 

EXAMPLE (^2) What number is 84% of 500?
StrategyWe will identify the percent, the base, and
the amount and write a percent proportion of the form
.
WHYThen we can solve the proportion to find the
unknown number.
SolutionFirst, we write the percent proportion.
is of
This is the proportion to solve.
To make the calculations easier, it is helpful to simplify the ratio at this time.
On the right side, simplify:.
Recall from Section 5.2 that to solve a proportion we use the cross products.
Find the cross products:.
Then set them equal.
To simplify the right side of the equation,
do the multiplication: 500  21 10,500.
To undo the multiplication by 25 and isolate xon
the left side, divide both sides of the equation
by 25. Then remove the common factor of 25 from
the numerator and denominator.
On the right side, divide 10,500 by 25.
We have found that 420 is 84% of 500. That is, 420 union members mentioned in the
newspaper article voted to accept the new offer.
x 420
x 25
1
25
1



10,500

25

x 25 10,500

x

500 

21

x 25  500  21 25

84

100



4

1

 21

4

1

 25



21

25

x

500



21

25

10084

x

500



84

100

amount percent base

What number 84% 500?

amountbase percent 100

Circulation Monday, March 23 50 cents

Transit Strike Averted!

Drinking Water38 of 40 Wells

Declared Safe

500-member unionLabor: 84% of

votes to acceptnew offer

New Appointees

These six area residentsnow make up 75% of the

State Board of Examiners

500

 21

500

10 000

10,500

420

25  10,500

 10 0

50

 50

00

 0

0

2 Solve percent proportions to find the amount.

Recall the labor union problem from the newspaper example in the introduction to

this section. We can write and solve a percent proportion to find the unknown amount.







c. of is

366

x



165

100

percent base amount

165% what number 366?