Nick wants to join a gym, and he is deciding between two options. Infinity Fitness charges $\$45$ per month, plus a one-time registration fee of $\$20$ . The Power Zone charges $\$37.50$ per month, plus a one-time registration fee of $\$65$ . Which equation can you use to find $m$ , the number of months it would take for the total cost at either gym to be the same? $\newline$ Choices: $\newline$ (A) $20 + 45m = 65 + 37.5m$ $\newline$ (B) $20m + 45 = 60m + 37.5$ $\newline$ After how many months would the total cost at either gym be the same? $\newline$ $\_\_\_\_$ months $\newline$

Full solution

Q. Nick wants to join a gym, and he is deciding between two options. Infinity Fitness charges

\$45

per month, plus a one-time registration fee of

\$20

. The Power Zone charges

\$37.50

per month, plus a one-time registration fee of

\$65

. Which equation can you use to find

m

, the number of months it would take for the total cost at either gym to be the same?

\newline

Choices:

\newline

(A)

20 + 45m = 65 + 37.5m

\newline

(B)

20m + 45 = 60m + 37.5

\newline

After how many months would the total cost at either gym be the same?

\newline

\_\_\_\_

months

\newline

Set up equation: Set up the equation for the total cost of each gym. $\newline$ For Infinity Fitness, the total cost after $m$ months is the monthly fee times the number of months plus the one-time registration fee: Total cost = $45m + 20$ . $\newline$ For The Power Zone, the total cost after $m$ months is the monthly fee times the number of months plus the one-time registration fee: Total cost = $37.5m + 65$ .
Write equation for total cost: Write the equation to find the number of months when the total cost for both gyms is the same. $\newline$ This means setting the total cost of Infinity Fitness equal to the total cost of The Power Zone: $45m + 20 = 37.5m + 65$ .
Identify correct equation: Identify the correct equation from the given choices that matches the equation from Step $2$ . $\newline$ The correct equation is (A) $20 + 45m = 65 + 37.5m$ .
Solve for number of months: Solve the equation for $m$ to find out after how many months the total cost at either gym would be the same. $\newline$ Subtract $37.5m$ from both sides of the equation: $45m - 37.5m + 20 = 65$ . $\newline$ Combine like terms: $7.5m + 20 = 65$ . $\newline$ Subtract $20$ from both sides: $7.5m = 45$ . $\newline$ Divide both sides by $7.5$ : $m = 45 / 7.5$ . $\newline$ Calculate the value of $m$ : $m = 6$ .