Question

3. A cell phone company offers two texting plans. People who use plan A pay 10 cents

for each text sent or received. People who use plan B pay 12 dollars per month, and
then pay an additional 2 cents for each text sent or received.
a. Write an inequality to represent the fact that it is cheaper for someone to use
plan A than plan B. Use x to represent the number of texts they send.
b. Solve the inequality.

Answer 1

Plan A: 0.10x

Plan B: 12 + 0.02x

It greatly depends on how many texts they receive each month. If they send or receive only 50 text messages a month, plan A will be the plan to go with. They will pay $5.00 for plan A and they would pay $13 for plan B. If they send or receive 1000 text messages a month, plan B will be the plan to go with. They will pay $100.00 for plan A and they would pay $32 for plan B.

0.10x = 12 + 0.02x

-11.90x = 0.02x

x = 150

For you to want plan A, the inequality would be x < 150 and for you to want plan B, the inequality would be x > 150. In other words, you must send or receive less than 150 text messages to want plan A and you must send or receive over 150 text messages for you to want plan B.

Hope this helps!

Answer 2

a. 0.10x < 12 + 0.02x

b. x < 150

Explanation:

a. For sending x texts, the cost of Plan A in dollars is ...

0.10x

For sending x texts, the cost of Plan B in dollars is ...

12 + 0.02x . . . . . . where 12 is the monthly charge regardless of texts sent

We want the Plan A charge to be less than the Plan B charge, so the inequality is ...

0.10x < 12 + 0.02x

__

b. Subtract 0.02x:

0.08x < 12

Divide by 0.08

x < 12/0.08

x < 150 . . . . . the solution to the inequality