Algebra 1 Common Core Student Edition, Grade 8-9

H o w is this p ro p o rtio n
different from others
you've seen?
This p ro p o rtio n looks
more complex, but the
Cross Products P roperty
is tru e fo r any p ro p o rtio n.
Treat each n u m e ra to r as
a single variable when
you cross-multiply.

Solving a Multi-Step Proportion

What is the solution of the proportion h 5 8 = b 4 3?

b-8 = b + 3

5 4

4[b - 8 ) = 5(b + 3)

4b - 32 = 5b + 15

4b - 32 - 4b = 5b + 15 - 4b

-3 2 = b + 15

—4 7 = b

Cross Products Property

Distributive Property

Subtract 4b from each side.

Simplify.

Subtract 15 from each side and simplify.

G o t It? 3. W hat is th e solution of the pro p o rtio n |

W hen you m odel a real-w orld situation w ith a proportion, you m u st write the

pro p o rtio n carefully. You can write th e p ro p o rtio n so th at the n u m erato rs have the

sam e u nits an d th e d en o m in ato rs have th e sam e units.

Correct:^1002 h mi. xm i 5 h Incorrect:^1002 h mi. 5 h xm i

Pr o b l em 4 Using a Proportion to Solve a Problem

Is th e r e o n ly o n e

way to write a

proportion?

No. You can w rite o th e r

proportions to solve the

problem. For exam ple,

2 gigabytes _ 500 songs

80 gigabytes — s songs

also works.

Music A portable media player has 2 gigabytes of storage and can hold about

500 songs. A similar but larger media player has 80 gigabytes of storage. About

how many songs can the larger media player hold?

• Smaller media player has
  2 gigabytes and can hold
  500 songs


• Larger media player has
  80 gigabytes

^le e d

The num ber o f songs

the larger player

can hold

Plan

Write a proportion to model the

s itu a tio n. You can set up th e

proportion so that the numerators

have the same units and the

denominators have the same

units. Then solve th e p ro p o rtio n.

Write a proportion.

2 gigabytes 80 gigabytes

500 songs — s songs

2s = 5 0 0(80) Cross Products Property

2s = 4 0,0 00 M ultiply.

s = 2 0 ,0 0 0 Divide each side by 2 and simplify.

The larger m edia player can h old 20,000 songs.

G o t It? 4. An 8 -oz can of orange juice contains ab o u t 97 m g of vitam in C. About how

m any m illigrams of vitam in C are th ere in a 12-oz can of orange juice?

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