Question

here are two cell phone planes.

• plan a costs $70 per month and comes with a free phone worth $500.
• plan b costs $50 per month, but doesnt come with a free phone.

if you choose plan b and buy a $500 phone, after how many months will your total cost be the same as the cost of choosing plan a?

Explanation:

Step1: Set up cost equations

Let \(x\) be the number of months.
For Plan A, the cost \(C_A = 70x\) (since the phone is free).
For Plan B, the cost \(C_B=50x + 500\) (monthly cost plus phone cost).

Step2: Set \(C_A = C_B\) and solve for \(x\)

Set \(70x=50x + 500\).
Subtract \(50x\) from both sides: \(70x-50x=50x + 500-50x\).
We get \(20x=500\).
Divide both sides by \(20\): \(x=\frac{500}{20}\).

Answer:

\(25\)