Question

Option 1: $30 per month and $100 membership fee. Option 2: $25 per month and $150 membership fee. Michael is trying to determine which tennis club to join. If Michael choose option 2 for which month will his total cost for option 2 be less than total cost for option 1? A. month 8. B. month 9 C. month 10 D. month 11

Answer 1

D) month 11

Explanation:

The solution is month 11. To solve this problem set up the inequality

25x + 150 < 30x + 100

The result is x > 10. In month 10, the costs will be equal, but in month 11, the total cost of option 2 is less than the total cost of option 3.

Answer 2

Let x = the number of months.

Option 1:
Membership fee = $100
Monthly cost = $30
Total cost = 100 + 30x

Option 2:
Membership fee = $150
Monthly cost = $25
Total cost = 150 + 25x

We want the cost for option 2 to be less than that for option 1.
Therefore
150 + 25x < 100 + 30x
50 < 5x
10 < x
or
x > 10 months

Answer: C. month 10