Question

you are choosing between two health clubs. club a offers membership for a fee of $24 plus a monthly fee of $18. club b offers membership for a fee of $12 plus a monthly fee of $22. after how many months will the total cost of each health club be the same? what will be the total cost for each club? in \\(\square\\) months the total cost of each health club will be the same. the total cost for each health club will be $\square.

Explanation:

Step1: Define variables and cost functions

Let $m$ = number of months.
Total cost for Club A: $C_A = 24 + 18m$
Total cost for Club B: $C_B = 12 + 22m$

Step2: Set costs equal to solve for $m$

Set $C_A = C_B$:
$$24 + 18m = 12 + 22m$$
Subtract $18m$ from both sides:
$$24 = 12 + 4m$$
Subtract 12 from both sides:
$$12 = 4m$$
Divide by 4:
$$m = \frac{12}{4} = 3$$

Step3: Calculate total cost at $m=3$

Substitute $m=3$ into $C_A$:
$$C_A = 24 + 18(3) = 24 + 54 = 78$$

Answer:

In 3 months the total cost of each health club will be the same.
The total cost for each health club will be $\$78$.