Joey wants to buy a gym membership. He visits two gyms with two different
fees. Gym A has a $40 sign up fee and it costs $25 per month. Gym B has a $50
sign up fee and costs $20 per month. How many months will he have to belong
at each before the costs are the same?
Where's the answer
Membership to a local gym costs a one-time fee of $25 and $20 per month. Let c=the total cost for membership and m=the number of months. Which equation can be used to calculate the total cost for gym membership?
To determine the number of months Joey will have to belong at each gym before the costs are the same, we can set up an equation.
Let's let 'x' represent the number of months.
For Gym A, the total cost is given by:
Total cost for Gym A = $40 (sign-up fee) + $25 (monthly fee) * x (number of months)
For Gym B, the total cost is given by:
Total cost for Gym B = $50 (sign-up fee) + $20 (monthly fee) * x (number of months)
We want to find the number of months where the total costs are the same:
Total cost for Gym A = Total cost for Gym B
Setting up the equation:
$40 + $25x = $50 + $20x
To solve for 'x' (number of months), we can subtract $20x from both sides and then subtract $40 from both sides:
$25x - $20x = $50 - $40
$5x = $10
Dividing both sides by $5, we get:
x = 2
Therefore, Joey will have to belong to each gym for 2 months before the costs are the same.
To determine how many months Joey will have to belong at each gym before the costs are the same, we need to set up an equation and solve for the number of months.
Let's assume Joey belongs to Gym A for x months and Gym B for y months.
For Gym A, the cost will be:
Total cost for Gym A = Sign up fee for Gym A + Monthly fee for Gym A * Number of months
Total cost for Gym A = $40 + ($25 * x)
For Gym B, the cost will be:
Total cost for Gym B = Sign up fee for Gym B + Monthly fee for Gym B * Number of months
Total cost for Gym B = $50 + ($20 * y)
To find the point where the costs are the same, we need to set the two equations equal to each other:
$40 + ($25 * x) = $50 + ($20 * y)
Now, we can simplify the equation and solve for x and y:
$25 * x - $20 * y = $50 - $40
$25 * x - $20 * y = $10
To make it easier, let's divide the equation by $5:
5x - 4y = 2
Now, let's look for possible values of x and y that satisfy this equation. We can start by setting x = 1 and finding the corresponding value of y:
5(1) - 4y = 2
5 - 4y = 2
-4y = 2 - 5
-4y = -3
y = (-3) / (-4)
y = 3/4
So, if Joey belongs to Gym A for 1 month and Gym B for 3/4 of a month, the costs will be the same. However, it's not possible to have a fraction of a month, so we need to round up to the nearest whole month.
Therefore, Joey would have to belong to each gym for at least 1 month before the costs are the same.