One gym charges $40 per month and $3 per exercise class. Another gym charges $20 per month and $8 per exercise class. After how many exercise classes will the monthly cost be the same and what will that cost be?

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Answer 1 · 2017-04-18T04:39:30

#4# classes
Cost # = $52#

You have basically two equations for cost at the two different gyms:

#"Cost"_1 = 3n + 40 " and Cost"_2 = 8n + 20#
where #n = # the number of exercise classes

To find out when the cost will be the same, set the two cost equations equal to each other and solve for #n#:

#3n + 40 = 8n + 20#

Subtract #3n# from both sides of the equation:

#3n - 3n + 40 = 8n - 3n + 20#

#40 = 5n + 20#

Subtract #20# from both sides of the equation:

#40 - 20 = 5n + 20 - 20#

#20 = 5n#

#n = 20/5 = 4# classes

Cost #= 3(4) + 40 = 52#
Cost #= 8(4) + 20 = 52#