Question

under his cell phone plan, mamadou pays a flat cost of $52 per month and $3 per gigabyte, or part of a gigabyte. (for example, if he used 2.3 gigabytes, he would have to pay for 3 whole gigabytes.) he wants to keep his bill under $65 per month. what is the maximum whole number of gigabytes of data he can use while staying within his budget?

Explanation:

Step1: Set up the inequality

Let \(x\) be the number of gigabytes. The cost function is \(C = 52+3x\). We want \(C<65\), so \(52 + 3x<65\).

Step2: Solve the inequality for \(x\)

Subtract 52 from both sides: \(3x<65 - 52\), so \(3x<13\). Then divide by 3: \(x<\frac{13}{3}\approx4.33\).

Since \(x\) is a whole number and if \(x = 4\), \(C=52+3\times4=52 + 12=64<65\), and if \(x = 5\), \(C=52+3\times5=52+15 = 67>65\)

Answer:

4