Question

your cell - phone plan costs $2.90 per month plus $0.18 for each text message you send or receive. you have at most $20 to spend on your cell phone bill. what is the maximum number of text messages that you can send or receive next month? the maximum number of text messages is

Explanation:

Step1: Set up an inequality

Let $x$ be the number of text - messages. The cost of the cell - phone plan is $7.90$ per month plus $0.18$ for each text message. The total cost $C$ is $C = 7.90+0.18x$. We know that we have at most $20$ to spend, so the inequality is $7.90 + 0.18x\leq20$.

Step2: Solve the inequality for $x$

First, subtract $7.90$ from both sides of the inequality:
$0.18x\leq20 - 7.90$.
$0.18x\leq12.1$.
Then, divide both sides by $0.18$:
$x\leq\frac{12.1}{0.18}\approx67.22$.

Step3: Determine the maximum number of text - messages

Since $x$ represents the number of text - messages and it must be an integer, the maximum value of $x$ is $67$.

Answer:

$67$