Question

3. A cell phone company offers two texting plans. People who use plan A pay10 cents for each text sent or received. People who use plan B pay 12 dollarsper month, and then pay an additional 2 cents for each text sent or received.3a. Write an inequality to represent the fact that it is cheaper for someoneto use plan A than plan B. Use x to represent the number of texts theysend.Your answer3b. Solve the inequality."O x> 150O x < 150O > 1.5O x< 1.5

Answer 1

The Solution:

Given:

Plan A:

Each text sent or received cost $0.10.

If x=number of texts sent or received in a month, the total cost is:

$0.1x$

Plan B:

Users pay a fixed charge of $12 and an additional $0.02 for each text sent or received. So, we have the expression for the total charges as:

$\begin{gathered} 12+0.02x \\ \text{ where x = number of texts sent or received.} \end{gathered}$

Part (a)

Writing the inequality that shows that to use plan A is cheaper than using plan B, we have:

$0.1x<12+0.02x$

Part (b)

Solving the inequality in part (a) above, we have:

$\begin{gathered} 0.1x<12+0.02x \\ \text{ Collecting the like terms, we get} \\ 0.1x-0.02x<12 \end{gathered}$$0.08x<12$

Dividing both sides by 0.08, we have:

$\begin{gathered} x<\frac{12}{0.08} \\ \\ x<150 \end{gathered}$

Therefore, the correct answer is [option 2]