a gym membership charges an initial fee for $100 plus a $25 free every month another gym charges $45 every month after how many months will the total cost for both gyms be the same
100 + 25m = 45m
Solve for m.
25 multiply 0.2 plus 100 equal 105
45 multiply 0.2 equal 9
5 months
To find the number of months when the total cost for both gyms will be the same, we need to set up an equation and solve for the number of months.
Let's assume the number of months is represented by 'x'.
For the first gym, the total cost after x months can be calculated as follows:
Total cost for the first gym = Initial fee + (Monthly fee * Number of months)
Total cost for the first gym = $100 + ($25 * x)
For the second gym, the total cost after x months is given by:
Total cost for the second gym = Monthly fee * Number of months
Total cost for the second gym = $45 * x
Now, we can set up an equation to find the number of months when the total cost for both gyms is the same:
$100 + ($25 * x) = $45 * x
To solve this equation, we can simplify it as follows:
$100 + $25x = $45x
Subtracting $25x from both sides:
$100 = $45x - $25x
Combining like terms:
$100 = $20x
Dividing both sides by $20:
x = $100 / $20
Calculating the value:
x = 5
Therefore, the total cost for both gyms will be the same after 5 months.