Question

You are choosing between two health clubs. Club A offers membership for a fee of $ 17 plus a monthly fee of $22. Club B offers membership for a fee of $13 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

Answer:

• 2 months
• $61 (for two months)

Step-by-step explanation:

Club B's savings of $17 - 13 = $4 in fee is eaten up at the rate of $24 -22 = $2 per month in monthly fees. It will take $4/($2/mo) = 2 mo for the total costs to be equal.

After 2 months, the amount at each club will be ...

• $17 + 22×2 = $61
• $13 + 24×2 = $61

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If you want to write equations, the club costs (a and b) in terms of months (m) of membership are ...

  a = 17 +22m

  b = 13 +24m

The difference is zero when ...

  a - b = 0

  (17 +22m) -(13 +24m) = 0

  4 -2m = 0 . . . . . . . simplify

  4 = 2m . . . . . . . . . add 2m . . . Note that 4 is 17-13; 2 is 24-22, as above.

  4/2 = m = 2 . . . . . . divide by the coefficient of m

The difference in total cost will be zero after 2 months.