Question

here are two cell phone plans.

• 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

Let \( m \) be the number of months. The total cost for Plan A is \( 70m \) (since it's $70 per month with a free phone worth $500, so we only consider the monthly cost). The total cost for Plan B is \( 50m + 500 \) ( $50 per month plus the $500 phone).

Step2: Set up the equation

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

Step3: Solve for \( m \)

Subtract \( 50m \) from both sides: \( 70m - 50m = 500 \), which simplifies to \( 20m = 500 \). Then divide both sides by 20: \( m=\frac{500}{20}=25 \).

Answer:

25