Algebra Demystified 2nd Ed

Chapter 9 linear inequaliTieS 327

4. Let x = number of tee shirts sold per month
   18 x = revenue

1500 + 8x = overhead costs + production costs = total cost
18 x – (1500 + 8x) = profit

profit ≥ 3500

18 –  +   ≥ 

– 

xx

x

 (  )

1500 8 3500

18 1500  

–   ≥ 

–   ≥ 

++

 ≥ 

8 3500

10 1500 3500

1500 1500

10 5

x

x

x^0000

5000

10

500

x

x

 ≥ 

 ≥ 

At least 500 tee shirts would need to be sold each month to make a
monthly profit of at least $3500.

5. Let x = number of average daily miles

The $24 option costs 24 + 0.80x per day (on average).

24 08040

24 24

08016

16

080

 .

. 

.

+  ≤ 

––

≤ 

≤ 

x

x

x

The most a customer could drive is an average of 20 miles per day in
order for the $24 plan to cost no more than the $40 plan.

6. Let x represent the number of minutes of service used in a month. The
   monthly cost for the unlimited plan is 75, and the monthly cost for the
   other plan is 15  .+  020 x. The unlimited plan is less expensive than the
   other when 15  .+  0207 x .>  5
   15 02075
   02060
   60
   020
   300

 .

. 

.

+  > 

> 

> 

> 

x

x

x

x

A customer would need to use more than 300 minutes or 5 hours of
the phone and web service per month in order to make the unlimited
plan less expensive.