Veronica is choosing between two health clubs. After how many months will the total cost for each health club be the same?

Understand the Problem

The question is asking for the number of months after which the total costs of two different health club memberships will be equal. To solve this, we need to set up an equation based on the membership fees and monthly costs of each club.

Answer

The total costs will be the same after $4$ months.

Steps to Solve

Set up the equation for costs of Yoga Studio A

The total cost for Yoga Studio A can be represented as: $$ C_A = 22 + 24.50m $$ Where:

(22) is the membership fee
(24.50) is the monthly fee
(m) is the number of months

Set up the equation for costs of Yoga Studio B

The total cost for Yoga Studio B can be represented as: $$ C_B = 47 + 18.25m $$ Where:

(47) is the membership fee
(18.25) is the monthly fee

Set the two cost equations equal to each other

To find when the total costs are the same, set the equations from steps 1 and 2 equal: $$ 22 + 24.50m = 47 + 18.25m $$

Solve for (m)

Subtract (18.25m) from both sides: $$ 22 + 6.25m = 47 $$

Now isolate (m) by subtracting (22) from both sides: $$ 6.25m = 25 $$

Finally, divide both sides by (6.25): $$ m = 4 $$

The total costs for both health clubs will be the same after $m = 4$ months.

More Information

After 4 months, the costs of both Yoga Studio A and Yoga Studio B will equal, meaning Veronica can make an informed decision about which membership to continue based on her preferences.

Tips

Forgetting to include the initial membership fee when calculating total costs.
Not properly grouping and isolating terms on one side of the equation when solving for (m).

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