Question

Alfonso wants to purchase a pool membership for the summer. He has no more than y dollars to

spend. The Aquatics Club charges an initial fee
of $75 plus $20 per month. The Swimming Hole
charges an initial fee of $15 plus $65 per month.
Write a system of inequalities that you can use to
determine which company offers the better deal.
Let x represent the number of months.

Answer 1

Let A represent the cost of purchasing a pool membership from the Aquatics Club and let S represent the cost of purchasing a pool membership from the Swimming Hole. Then, we can write the following system of inequalities:

A ≤ y

A = 75 + 20x

S ≤ y

S = 15 + 65x

The first two inequalities represent the cost of purchasing a membership from the Aquatics Club, while the last two represent the cost of purchasing a membership from the Swimming Hole. The inequalities ensure that the cost of purchasing a membership from either company does not exceed Alfonso's budget of y dollars.