How many months will he have to belong at each before the costs are the same

Question

JJoey wants to buy a gym membership he visited two gyms with two different fees gym A has a $40 sign up fee and it cost $25 per month. Gym B has a $50 sign up fee and it cost $20 per month

Answer 1

Let C_A be the Cost for Gym A and C_B be the cost for Gym B and m be the number of months.

CA = 40 + 25m

CB = 50 + 20m

We want to know when CA = CB so we set the two equations equal to each other.

40 + 25m = 50 + 20m

subtract 20m from both sides to get:

40 + 5m = 50

subtract 40 from both sides to get:

5m = 10

divide both sides by 5 to get:

m = 2 so in 2 months both total costs will be the same.

For gym A, you would have spent $40 to sign up and then 2 months at $25 each would be an additional $50 for a total of $90. For gym B, you would have spent $50 to sign up and then an additional $20 for 2 months for a total of $90.