Question

a cell phone provider is offering an unlimited data plan for $70 per month or a 5 gb plan for $55 per month. however, if you go over your 5 gb of data in a month, you have to pay an extra $10 for each gb. how many gb would be used to make both plans cost the same?

Explanation:

Step1: Set up equations

Let \(x\) be the total GB used.
For the unlimited plan, cost \(C_1 = 70\).
For the 5 - GB plan, cost \(C_2=55 + 10(x - 5)\).

Step2: Solve for \(x\)

Set \(C_1 = C_2\), so \(70=55 + 10(x - 5)\).
First, expand the right - hand side: \(70=55+10x-50\).
Simplify: \(70 = 10x + 5\).
Subtract 5 from both sides: \(70 - 5=10x\), so \(65 = 10x\).
Divide both sides by 10: \(x=\frac{65}{10}=6.5\).

Answer:

\(6.5\) GB.