Question

1. a cell company offers phone service for $15.00 a month plus $0.15 per call. if your budget allows you to spend at most $23 on phone service, what is the maximum number of calls you can make each month?

Explanation:

Step1: Set up the inequality

Let \(x\) be the number of calls. The cost function is \(C = 15+0.15x\). Since the budget allows spending at most \(23\), we have the inequality \(15 + 0.15x\leq23\).

Step2: Solve for \(x\)

Subtract \(15\) from both sides: \(0.15x\leq23 - 15\), so \(0.15x\leq8\).
Then divide both sides by \(0.15\): \(x\leq\frac{8}{0.15}=\frac{8}{\frac{15}{100}}=\frac{8\times100}{15}=\frac{800}{15}\approx53.33\).

Since the number of calls \(x\) must be an integer, we take the floor of \(53.33\).

Answer:

\(53\)