Write a linear equation

One health club charges a monthly fee of $81 and an extra $5 for every visit. Another health club charges $86 per month and $4 for every visit. For how many visits will the monthly charge be the same? Suppose x is the number of visits per month. Write a linear equation, which will derive the solution for the problem.

x = number of visits per month
y = total monthly cost 

y = 5x + 81   {one health club charges monthly fee of $81 and $5 for each visit}
y = 4x + 86   {another club charges monthly fee of $86 and $4 for each visit} 

5x + 81 = 4x + 86   {the linear equation to find out when the charge will be the same}
x + 81 = 86   {subtracted 4x from each side}
x = 5   {subtracted 81 from each side} 

For 5 visits, the monthly charge (y) will be the same.


- Algebra House