Algebra 1 Common Core Student Edition, Grade 8-9

How can a model
help you w rite the
equation?
The model shows th a t
the cost o f the niece's
items plus the cost o f the
nephew's items is $67.
f..............^67 ..................-I
1 s + 4 [ 2s 1

^ Got II? 1. W hat is th e solution of each equation? C heck ea ch answer.

a. l l m - 8 - 6 m = 22 b. -2y + 5 + 5y = 14

Pr o b l em 2 So l v i n g a M u l t i - St ep Eq u at i o n

Concert Merchandise Martha takes her niece and nephew to a concert.

She buys T-shirts and bumper stickers for them. The bumper stickers

cost $1 each. Martha's niece wants 1 shirt and 4 bumper stickers, and her

nephew wants 2 shirts but no bumper stickers. If Martha's total is $67,

what is the cost of one shirt?

• Bumper stickers cost $1


• Niece's items: 1 shirt, 4 bumper
  stickers


• Nephew's items: 2 shirts


• Total spent: $67

The cost o f one shirt W rite and solve an equation

that models the situation.

cost of niece's cost of

Relate item s (1 shirt a n d plus n e p h e w ’s item s is

4 stickers) (2 shirts)

Define Let s = th e cost of one shirt.

Write (s + 4) + 2s

(s + 4) + 2s = 67

s + 2s + 4 = 67

3s + 4 = 67

3s+ 4 - 4 = 67- 4

3s = 6 3

3s _ 63

3 3

s= 21

O ne shirt costs $21.

total M artha

spent

67

Commutative Property of Addition

Combine like terms.

$ u b tra c t 4 fro m each side.

Simplify.

D ivide each side by 3.

Simplify.

si Got It? 2. Noah a n d Kate are sh opping for n ew guitar strings in a m usic store.

N oah buys 2 packs of strings. Kate buys 2 packs of strings an d a

m usic book. The b ook costs $16. Their total cost is $72. How much

is one pack of strings?

c

PowerAlgebra.com Lesso n 2-3 So l v i n g M u l t i - St e p Eq u a t i o n s^95