Irasema M.

asked • 12/08/16

A gym charges $45 to join plus $30 per month. Another gym charges $60 to join plus $20 per month. How many months can you be a member and the cost be the same

A gym charges $45 to join plus $30 per mont. Another gym charges $60 to join plus $20 per mont. How many months can you be a member and the cost be the same?

1 Expert Answer

By:

Gregg K. answered • 12/08/16

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Cost = 45 + 30M
 
Cost = 60 + 20M
 
Set equal to each other
 
45 + 30M = 60 + 20M
 
10M = 15
 
M = 1.5
 
both would cost 90 after 1.5 months, after that it would be more expensive to attend the gym with the higher monthly charge

We must also consider that 1.5 would not be possible since it is at a half month

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Andrew M.

Which basically means that, if we pay on a monthly basis,
the cost would never actually be equal.
Gym A: 30M + 45 = $75 for month 1
Gym B: 20M + 60 = $80 for month 1
 
Gym A after 2 months:  $105
Gym B after 2 months:  $100
 
If we split the monthly payments into
4 payments per month then the payment
Gym A = 30/4 = $7.5 per payment
Gym B = 20/4 = $5 per payment
 
7.5P + 45 ≤ 5P + 60
2.5P ≤ 15
P ≤ 15/2.5
P ≤ 6
 
Gym A costs less for first 5 payments, the same at payment 6
and as of payment 7 gym A costs more than gym B
 
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12/09/16

Andrew M.

Note that 6 payments, at 4 payments per month, equates to 1.5 months
which is the point at which the total payments for each gym are equal.
 
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12/09/16

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