Question

1. under her cell phone plan, autumn pays a flat cost of $46.50 per month and $5 per gigabyte. she wants to keep her bill under $60 per month. write and solve an inequality which can be used to determine g, the number of gigabytes autumn can use while staying within her budget. 2. under her cell phone plan, arianys pays a flat cost of $42 per month and $5 per gigabyte. she wants to keep her bill at $66 per month. how many gigabytes of data can she use while staying within her budget?

Explanation:

Problem 1

Step1: Define total cost

The total cost is flat cost plus cost per gigabyte. So total cost \( C = 46.50 + 5g \). We want \( C < 60 \), so the inequality is \( 46.50 + 5g < 60 \).

Step2: Solve for \( g \)

Subtract 46.50 from both sides: \( 5g < 60 - 46.50 \)
\( 5g < 13.50 \)
Divide both sides by 5: \( g < \frac{13.50}{5} \)
\( g < 2.7 \)

Step1: Define total cost equation

Total cost \( C = 42 + 5g \). We want \( C = 86 \), so the equation is \( 42 + 5g = 86 \).

Step2: Solve for \( g \)

Subtract 42 from both sides: \( 5g = 86 - 42 \)
\( 5g = 44 \)
Divide both sides by 5: \( g = \frac{44}{5} = 8.8 \)

Answer:

Inequality: \( 46.50 + 5g < 60 \), Solution: \( g < 2.7 \)

Problem 2