Algebra 1 Common Core Student Edition, Grade 8-9

Got It? 1. a. W hat is th e solution of 7k + 2 = 4k - 10?

b. Reasoning Solve th e eq u a tio n in P roblem 1 by subtracting 5x f r o m e a c h

side instead of 2x. C om pare an d co n trast your solution w ith the solution

in P roblem 1.

[hjnfc
How can a model
help you w rite the
equation?
The m odel show s th a t
the current design tim e
is equal to th e n e w
design tim e plus the 8 h
needed to learn the new
software.

1 1-5P I

I o s p r r n

Problem 2 Using an Equation With Variables on Both Sides

Graphic Design It takes a graphic designer 1.5 h to make one page of a Web site.

Using new software, the designer could complete each page in 1.25 h, but it takes

8 h to learn the software. How many Web pages would the designer have to make in

order to save time using the new software?

• Current design time:
  1.5 h per page


• Time with new software:
  1.25 h per page


• Time to learn software: 8 h

Relate

The num ber o f pages

the designer needs

to make for the new

software to save time

.f l a n...

Write and solve an equation

th a t models the situation.

current = design tim e w ith + time to learn

design tim e new software software

Define Let p = th e n u m b e r of pages th e designer n ee d s to m ake.

Write 1.5p = 1.25p + 8

1.5 p = 1.25 p + 8

1.5p - 1.25p = 1.25p + 8 - 1.25p

0.25 p = 8

0.25p

0.25

8

0.25

p = 32

Subtract 1,25p from each side.

Simplify.

Divide each side by 0.25.

Simplify.

It will take th e designer th e sam e a m o u n t of tim e to m ake 32 Web pages using either

software. The designer m u st m ake 33 pages or m ore in o rder to save tim e using the

new software.

Got It? 2. An office m an ag e r sp en t $650 on a new energy-saving copier th a t will

reduce th e m on th ly electric bill for th e office from $112 to $ 88. In how m any

m o n th s will th e copier pay for itself?

H PowerAigebra.com J^ | Lesson 2-4 So l v i n g Eq u a t i o n s W i t h V a r i a b l e s o n Bo t h Si d es. ......- - 103

---------------------------------------------------------------------------------------------------------------------------