One health club charges a monthly fee of $100 and an extra $5 for every visit. Another health club charges $103 per month and $4 for every visit. How many visits in a month would make the cost of each health club equal?
Suppose x is the number of visits per month. Fill in the blanks to write a linear equation, which will derive the solution for the problem. Then solve the equation for x to find the number of visits.
100 + 5 x = 103 + 4 x
Let's analyze the problem step by step.
First, we need to determine the cost of each health club based on the number of visits per month.
For the first health club, the monthly fee is $100, and there is an additional charge of $5 for every visit. Hence, the cost of the first health club can be represented by the equation:
Cost of first health club = $100 + ($5 * x)
For the second health club, the monthly fee is $103, and there is an additional charge of $4 for every visit. So, the cost of the second health club can be represented by the equation:
Cost of second health club = $103 + ($4 * x)
To find the number of visits that would make the cost of each health club equal, we need to set the two equations equal to each other:
$100 + ($5 * x) = $103 + ($4 * x)
Now, let's solve the equation for x:
$5 * x - $4 * x = $103 - $100
Simplifying the equation:
$x = $3
Therefore, the number of visits in a month that would make the cost of each health club equal is 3 visits.