Fitness center A has a $60 enrollment fee and costs $35 per month. Fitness center B has no enrollment fee and costs $45 per month. A) Identity the variables then write system of linear equations to represent the situation.

B) In how many months will both fitness centers cost the same? What will the cost be? Use the substitution method to solve this real-world application.

Given :

Fitness center A has a $60 enrollment fee and costs $35 per month. Fitness center B has no enrollment fee and costs $45 per month.

To Find :

A) Identity the variables then write system of linear equations to represent the situation.

B) In how many months will both fitness centers cost the same? What will the cost be? Use the substitution method to solve this real-world application.

Solution :

a) Linear equation of center A :

F = 35x + 60   ...1)

Linear equation of center B :

F = 45x  ...2)

b) Let, after n months both fitness centers cost the same fee :

So, 35m + 60 = 45m

10m = 60

m = 6 months

Putting value of m in equation 1) or 2) is :

F = (35×6) + 60 = $270 or F = 45×6 = $270 .

Therefore, the cost when they have same fee is $270 .

Hence, this is the required solution.