Members of the Lake Shawnee club pay $40 per summer season plus $7.50 each time they rent a boat. Nonmembers pay $12.50 each time they rent a boat. How many times would both a member and a nonmember have to rent a boat in order to pay the same amount?

40 + 7.5 x = 12.5 x

40 = 5 x

x = 8 times

To find the number of times that both a member and a nonmember would have to rent a boat in order to pay the same amount, we can set up an equation.

Let's assume the number of times they rent a boat is represented by "x".

For a member, the total cost is $40 for the summer season plus $7.50 per boat rental. So, the total cost for a member would be:

Total cost for a member = $40 + ($7.50 * x)

For a nonmember, the cost is $12.50 per boat rental. So, the total cost for a nonmember would be:

Total cost for a nonmember = $12.50 * x

Now, to find the number of times they would have to rent a boat to pay the same amount, we can set up an equation:

$40 + ($7.50 * x) = $12.50 * x

Now we can solve this equation:

$40 + $7.50x = $12.50x

Subtract $7.50x from both sides:

$40 = $12.50x - $7.50x

Combine like terms:

$40 = $5.00x

Now divide both sides by $5.00:

$40 / $5.00 = x

8 = x

Therefore, both a member and a nonmember would have to rent a boat 8 times in order to pay the same amount.

To determine the number of times a member and a nonmember would have to rent a boat to pay the same amount, we'll set up an equation.

Let's assume the number of times both a member and a nonmember rent a boat is represented by "x."

For a member:
Total cost = Membership cost + Boat rental cost
Total cost = $40 + $7.50x

For a nonmember:
Total cost = Boat rental cost
Total cost = $12.50x

Since we want the total cost to be the same for both a member and a nonmember, we can equate the two equations:

$40 + $7.50x = $12.50x

Now, we can solve for "x":

$40 = $12.50x - $7.50x
$40 = $5x

Dividing both sides by $5, we find that:

$x = 8

Therefore, both a member and a nonmember would have to rent a boat 8 times in order to pay the same amount.