Sarah and Joe are seeking to join a gym. Sarah saw on television that Great Gym is offering membership at $19.50 per month, plus a one-time registration fee of $59. Joe plans to join Wacky Workout World because Wacky Workout World only charges $9.50 per month, plus a one-time registration fee of $149.
Both gym memberships will eventually have a month in which the cost to attend either gym would be the same. How long would this membership be and how much would it cost? Show your work.
Using the functions I already gave you:
G = 59.00 + 19.50x
W = 149.00 + 9.50x
you want to find when the costs are equal. Well, duh -- set the two values equal and see which value of x makes it so:
59.00 + 19.50x = 149.00 + 9.50x
10x = 90
x = 9
To determine the month when the cost of membership at both gyms would 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 Sarah's Great Gym membership, the cost per month is $19.50 and there is a one-time registration fee of $59. So the total cost for Sarah's membership would be:
Total cost for Sarah's membership = (Monthly cost * Number of months) + Registration fee
Total cost for Sarah's membership = ($19.50 * x) + $59
For Joe's Wacky Workout World membership, the cost per month is $9.50 and there is a one-time registration fee of $149. So the total cost for Joe's membership would be:
Total cost for Joe's membership = (Monthly cost * Number of months) + Registration fee
Total cost for Joe's membership = ($9.50 * x) + $149
Since we want to find the month when the cost of membership at both gyms is the same, we can set up an equation by equating the total costs for Sarah and Joe:
($19.50 * x) + $59 = ($9.50 * x) + $149
Now, we can solve this equation to find the value of 'x', which represents the number of months:
$19.50x + $59 = $9.50x + $149
Subtract $9.50x from both sides:
$19.50x - $9.50x + $59 = $9.50x - $9.50x + $149
$10.00x + $59 = $149
Subtract $59 from both sides:
$10.00x = $149 - $59
$10.00x = $90
Divide both sides by $10.00:
x = $90 / $10.00
x = 9
Therefore, the cost of membership at both gyms would be the same after 9 months. To find the cost, we can substitute the value of 'x' back into either equation. Let's use Sarah's equation:
Total cost for Sarah's membership = ($19.50 * 9) + $59
Total cost for Sarah's membership = $175.50 + $59
Total cost for Sarah's membership = $234.50
So, after 9 months, the cost of membership at both gyms would be the same, and it would cost $234.50.