Question

(1) 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 data used in GB. For the 5GB plan, the cost function is \(C_1 = 55+10(x - 5)\) (when \(x>5\)). For the unlimited plan, \(C_2=70\).

Step2: Solve the equation

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

Answer:

\(6.5\)