Question

under his cell phone plan, julian pays a flat cost of $52 per month and $3 per gigabyte. he wants to keep his bill at $58 per month. which tape diagram could be used to represent the context if g represents the number of gigabytes of data julian can use while staying within his budget?

Explanation:

Step1: Determine the total cost formula

The total cost \( C \) is the sum of the flat cost and the cost per gigabyte. The flat cost is \( 52 \) dollars, and the cost per gigabyte is \( 3 \) dollars. If \( g \) is the number of gigabytes, then \( C=52 + 3g \). We want \( C = 58 \). So, \( 58=52+3g \).

Step2: Analyze each tape - diagram

• Option A: The total is \( 52 + 3g \), but the total shown is \( 55 \) (incorrect as we want \( 58 \)).
• Option B: The total is \( 52+3g \), but the total shown is \( 55 \) (incorrect).
• Option C: The total is \( 3g+52 \). If \( 3g + 52=58 \), solving for \( g \): \( 3g=58 - 52=6 \), \( g = 2 \). The tape - diagram has \( 3\)s and a \( 52\) with a total of \( 58 \).
• Option D: The total is \( 3g+52 \), but the total shown is \( 58 \) with the wrong arrangement (the \( 3\)s and \( 52\) are not in the correct additive order for the cost formula \( C = 52+3g \)).

Answer:

C