Answer to Question #93833 in Algebra for Lily ponds

Question

Michael is trying to determine which tennis club to join. If Michael chooses option 2, for which month will his total cost for option 2 be less than his total cost for option 1? A) month 8 B) month 9 C) month 10 D) month 11

Answer 1

Below is the full text of the problem, and now it makes sense:

• 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 chooses option 2, for which month will his total cost for option 2 be less than his total cost for option 1?

Solution

For $n$ months for each option the total cost will be

$$C_1=100+30n,\\ C_2=150+25n,\\ C_2<C_1,\\ 150+25n<100+30n,\\ n>\frac{150-100}{30-25}=10.$$

We see that beginning with the month after the 10th (since we solved strict inequality), the total cost of the second option becomes less than the total cost for the first option. It's the 11th month.