You are choosing between two health clubs. Club A offers membership for a fee of $10 plus $15 per month. Club B offers membership for a fee of $25 plus $12 per month. After how many months will the total cost of each health club be the same? (1 point)

Question

In months the total cost of each health club will be the same.

Answer 1

To find out after how many months the total cost of each health club will be the same, we can set up equations for the total cost of each club.

Let \( x \) be the number of months.

For Club A:

• Initial fee = $10
• Monthly fee = $15
• Total cost for \( x \) months = \( 10 + 15x \)

For Club B:

• Initial fee = $25
• Monthly fee = $12
• Total cost for \( x \) months = \( 25 + 12x \)

To find out when the costs are the same, we set the two equations equal to each other:

\[ 10 + 15x = 25 + 12x \]

Now, let's solve for \( x \):

1. Subtract \( 12x \) from both sides:

\[ 10 + 15x - 12x = 25 \]

This simplifies to:

\[ 10 + 3x = 25 \]

2. Next, subtract 10 from both sides:

\[ 3x = 15 \]

3. Finally, divide both sides by 3:

\[ x = 5 \]

Thus, after 5 months, the total cost of each health club will be the same.