Question

7. Veronica is choosing between two health clubs.

After how many months will the total cost for
each health club be the same?

Answer 1

The total cost for each health club will be the same after 4 months.

Explanation:

• Let A = membership fee for studio A

• B = membership fee for studio B

• x= membership month

• 
  `A = 22 + 24.5x`

• 
  `B = 47.00 + 18.25x`

We want to when the total cost at each health studio is the same.

In other words, when A = B.

Therefore, the expression becomes

`A = B`

`22\:+\:24.5x=47.00\:+\:18.25x`

Step 1: Simplify both sides of the equation.

`24.5x+22=18.25x+47`

Step 2: Subtract 18.25x from both sides.

`24.5x+22-18.25x=18.25x+47-18.25x`

`6.25x+22=47`

Step 3: Subtract 22 from both sides.

`6.25x+22-22=47-22`

`6.25x=25`

Step 4: Divide both sides by 6.25

`(6.25x)/(6.25)=(25)/(6.25)`

`x=4`

Therefore, the total cost for each health club will be the same after 4 months.