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: Define variables and costs

Let \( m \) be the number of months. The total cost for Plan A is always \( \$70m \) (since the phone is free). For Plan B, the total cost is the monthly cost plus the phone cost, so it's \( \$50m + \$500 \).

Step2: Set up the equation

We want to find when the costs are equal, so set \( 70m = 50m + 500 \).

Step3: Solve for \( m \)

Subtract \( 50m \) from both sides: \( 70m - 50m = 500 \)
Simplify: \( 20m = 500 \)
Divide both sides by 20: \( m = \frac{500}{20} = 25 \)

Answer:

25