Question

1. priyas cell phone plan costs $35 each month plus $15 for each gigabyte of data she uses. hans plan costs $75 each month, plus $5 for each gigabyte of data. is there a number of gigabytes of data for which the plans cost the same amount? how many gigabytes will they use to pay the same amount? (addressing nc.8.ee.7)

Explanation:

Step1: Set up equations

Let \(x\) be the number of gigabytes. Priya's cost \(C_{P}=35 + 15x\). Han's cost \(C_{H}=75+5x\).

Step2: Set the equations equal

Set \(C_{P}=C_{H}\), so \(35 + 15x=75+5x\).

Step3: Solve for \(x\)

Subtract \(5x\) from both sides: \(35 + 15x-5x=75+5x - 5x\), which gives \(35+10x = 75\).
Subtract \(35\) from both sides: \(10x=75 - 35\), so \(10x=40\).
Divide both sides by \(10\): \(x=\frac{40}{10}=4\).

Answer:

\(4\) gigabytes.