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.

Explanation:

Step1: Define the cost function

The total cost is the flat cost plus the cost per gigabyte times the number of gigabytes. So the inequality is $46.50 + 5g < 60$.

Step2: Subtract 46.50 from both sides

Subtract 46.50 from each side of the inequality: $5g < 60 - 46.50$. Calculate the right side: $5g < 13.50$.

Step3: Divide by 5

Divide both sides by 5: $g < \frac{13.50}{5}$. Calculate the right side: $g < 2.7$.

Answer:

The inequality is $46.50 + 5g < 60$ and the solution is $g < 2.7$, meaning Autumn can use less than 2.7 gigabytes.