Algebra 1 Common Core Student Edition, Grade 8-9

Thin k s—
How can a model
help you visualize the
proportion?
Use a m odel like the
one b e lo w t o visualize
any p e rcent p roblem. A
m odel fo r th e p ro p o rtio n
42-JLis 56 ' 100 l:>
0 42 56

0 % p% 100%

Problem 1 Finding a Percent Using the Percent Proportion

What percent of 56 is 42?

Write the percent proportion.

Substitute 42 for a and 56 for b.

Cross Products Property

Multiply.

Divide each side by 56.

P

100

P

100

42(100) = 56p

a

b

42

56

4200 = 56p

75 = p

42 is 75% of 56.

t

Got It? 1. W hat p ercen t of 90 is 54?

Think |M |

Is this p ro b lem re la te d

to other problems

you've seen?

Yes. This pro ble m is

related to Problem 1.

Both involve finding a

percent, b u t th e y use

different methods.

In Problem 1, you u sed th e p ercen t p ro p o rtio n | = Joq to find a percent. W hen you

write as p% a n d solve for a, you get the eq u a tio n a = p% • b. This eq u a tio n is called

the p ercen t equation. You can use either th e p ercen t eq u a tio n or th e p ercen t pro p o rtio n

to solve any percent problem.

Key Concept The Percent Equation

You can rep resen t “a is p p ercen t of b" using th e p ercen t eq u a tio n show n below. In the

equation, a is a p art of th e base b.

Algebra a = p% • b, where b + 0

Example W hat p ercen t of 50 is 25?

25 = p% • 50

Finding a Percent Using the Percent Equation

What percent of 40 is 2.5?

a = p% • b Write the percent equation.

2.5 = p% • 40 Substitute 2.5 fo r a and 40 fo r b.

0.0625 = p% Divide each side by 40.

6.25% = p% Write the decimal as a percent.

2.5 is 6.25% of 40.

G ot It? 2. R e a s o n i n g W hat p ercen t of 84 is 63? Use th e p ercen t eq u a tio n to solve.

Then use th e p ercen t proportion. C om pare your answers.

138 Ch ap t er 2 So l v i n g Eq u a t i o n s