Under her cell phone plan, Piper pays a flat cost of $38.50 per month and $5 per gigabyte, or part of a gigabyte. (For example, if she used 2.3 gigabytes, she would have to pay for 3 whole gigabytes.) She wants to keep her bill under $60 per month. What is the maximum whole number of gigabytes of data she can use while staying within her budget?

1 answer

To find out the maximum whole number of gigabytes of data Piper can use while keeping her monthly bill under $60, we can start by setting up an equation based on her cell phone plan.

The total cost \( C \) for her phone plan can be calculated using the formula: \[ C = 38.50 + 5n \] where \( n \) is the number of gigabytes used.

Piper wants her total cost to be less than $60, so we set up the inequality: \[ 38.50 + 5n < 60 \]

To solve for \( n \), we first subtract \( 38.50 \) from both sides: \[ 5n < 60 - 38.50 \] Calculating \( 60 - 38.50 \): \[ 60 - 38.50 = 21.50 \] Thus, we have the inequality: \[ 5n < 21.50 \]

Next, we divide both sides by \( 5 \): \[ n < \frac{21.50}{5} \] Calculating \( \frac{21.50}{5} \): \[ \frac{21.50}{5} = 4.30 \] Since \( n \) must be a whole number, we take the largest whole number less than \( 4.30 \), which is \( 4 \).

Now, we can double-check that this number keeps Piper's bill under $60:

  • If \( n = 4 \): \[ C = 38.50 + 5 \times 4 = 38.50 + 20 = 58.50 \] This is under $60.

  • If \( n = 5 \): \[ C = 38.50 + 5 \times 5 = 38.50 + 25 = 63.50 \] This exceeds $60.

Thus, the maximum whole number of gigabytes Piper can use while staying within her budget is \[ \boxed{4}. \]