Setting up a word problem

Question

A basic cellphone plan cost $25 per month for 60 calling minutes. Additional time cost $0.80 per minute. The formula C=25+0.80(x-60) gives the montly cost for this plan, C, for x calling minutes, where x>60. How many calling minutes are possible for a monthly cost of at least $89 and at most $137

Answer 1

Ben,

 

The monthly cost of at least $89 and at most $137, may be defined as:

 

89 ≤ C ≤ 137  

 

Since C = 25 + 0.80(x - 60), we get this compound inequality to solve:

 

89 ≤ 25 + 0.80(x - 60) ≤ 137  

 

(89 - 25) ≤ 0.80(x - 60) ≤ (137 - 25)

 

(89 - 25) ÷ 0.80 ≤ (x - 60) ≤ (137 - 25) ÷ 0.80

 

((89 - 25) ÷ 0.80) + 60 ≤ x ≤ ((137 - 25) ÷ 0.80) + 60

 

140 ≤ x ≤ 200

 

To get a monthly cost of at least $89 and at most $137, you may use at least 140 and at most 200 minutes per month.

 

Answer 2

C=25+0.80(x-60)

89<25+0.80(x-60)<137

89<25+0.8x-48<137

89<-23+0.8x<137

89+23<23-23+0.8x<+23+137

112<0.8x<160

1120<8x<1600

(1120/8)<(8x/8<(1600/8)

140<x<200

between 140 and 200 calling minutes, inclusive (140 and 200 are included)