Question

You are choosing between two health clubs. Club A offers membership for a fee

of $20 plus a monthly fee of $25. Club B offers membership for a fee of $25
plus a monthly fee of $24. After how many months will the total cost of each
health club be the same? What will be the total cost for each club?

Answer 1

Let:

x = Number of months

y1 = Total cost for Club A

y2 = Total cost for Club B

a = Fee of Club A per month

b = Fee of Club B per month

c = Initial fee of Club A

d = Initial fee of Club B

so:

`\begin{gathered} y1=ax+c \\ y1=25x+20 \\ -------- \\ y2=bx+d \\ y2=24x+25 \end{gathered}`

So, the total cost will be the same for:

`\begin{gathered} y1=y2 \\ 25x+20=24x+25 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 25x-24x=25-20 \\ x=5 \end{gathered}`

The cost will be the same for the month number 5. And the total cost will be:

`\begin{gathered} y1(5)=25(5)+20=145 \\ y2(5)=24(5)+25=145 \end{gathered}`

$145