Question

Write and solve an inequality for the situation. Tom is deciding whether he should become a member of a gym to use the basketball courts. The membership costs $135. Then, members will pay $3 each time they rent out the courts. Nonmembers can also rent the courts for $11 each time. How many times would Tom have to rent the basketball courts in order for his cost as a member to be cheaper than the cost of a nonmember? As a member, Tom's cost would be cheaper if he rents the courts or more times.​

Answer 1

As a member, Tom's cost would be cheaper if he rents the courts 17 or more times.

Explanation:

Let the number of times be x

If Tom is a member, and rents the courts x number of times, then he would pay

$135 + $3 × x = $135 + $3x

For a nonmember that rents x number of times, the nonmember would pay

$11 × x = $11x

Now, we are to determine which value of x for which $135 + $3x is less than $11x, that is

$135 + $3x < $11x

Solving the inequality,

$135 < $11x - $3x

$135 < $8x

$135 / $8 < x

16.875 < x

∴ x > 16.875

This means, for Tom's cost to be cheaper, he must have rented the court for more than 16.875 times. (Round 16.875 to the nearest whole number)

16.875 ≅ 17

∴ x > 17

Hence, As a member, Tom's cost would be cheaper if he rents the courts 17 or more times.