Question

Karly is choosing between two health clubs. Yoga Studio A charges a membership fee of $22.00 and $24.50 per month. Yoga Studio B charges a membership fee of $47.00 and $18.25 per month. At how many months will they cost the same? *

Answer 1

4 months

Explanation:

Given

Studio A

`Membership = \$22.00`

`Monthly = \$24.50`

Studio B

`Membership = \$47.00`

`Monthly = \$18.25`

Required

Determine when the cost will be the same

For both, we have the total cost to be:

`Cost = Membership + Monthly\ Cost * m`

Where m represents the number of month

For Studio A:

`Cost = 22 + 24.5 * m`

For Studio B:

`Cost = 47 + 18.25 * m`

Equate both expressions to get the required month

`47 + 18.25 * m = 22 + 24.5 * m`

`47 + 18.25 m = 22 + 24.5m`

Collect Like Terms

`47 - 22 = 24.5m - 18.25 m`

`25= 6.25m`

Reorder

`6.25m = 25`

Solve for m

`m = 25/6.25`

`m = 4`

Hence, it'll take 4 months