Question

you are choosing between two health clubs. club a offers membership for a fee of $24 plus a monthly fee of $16. club b offers membership for a fee of $16 plus a monthly fee of $17. after how many months will the total cost of each health club be the same? what will the total cost for each health club be? in months the total cost of each health club will be the same. the total cost for each health club will be $

Explanation:

Step1: Set up cost - equations

Let $m$ be the number of months. The cost of Club A, $C_A = 24 + 16m$. The cost of Club B, $C_B=16 + 17m$.

Step2: Set the two equations equal

We want to find when $C_A = C_B$, so $24 + 16m=16 + 17m$.

Step3: Solve for $m$

Subtract $16m$ from both sides: $24=16 + 17m-16m$. Simplify to get $24 = 16+m$. Then subtract 16 from both sides: $m=24 - 16=8$ months.

Step4: Find the total cost

Substitute $m = 8$ into either cost - equation. Using $C_A$: $C_A=24+16\times8=24 + 128 = 152$.

Answer:

8 months, $152$