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: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_____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 +24mThe 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 mThe difference in total cost will be zero after 2 months.