The ice rink sold 97 tickets for the afternoon session, for a total of
$765. General admission tickets cost
$10 and youth tickets cost
$5 each. How many of each kind of tickets were sold?
g = general admission
y = youth ticket
g + y = 97
10g + 5y = 765
g = 97 - y
10(97 - y) + 5y = 765
970 - 10y + 5y = 765
-5y = -205
y = 41
g + 41 = 97
g = 56
To determine the number of each kind of tickets sold, let's assume x represents the number of general admission tickets and y represents the number of youth tickets.
From the problem, we know that the ice rink sold a total of 97 tickets. Therefore, we have the equation:
x + y = 97 ----(1)
We also know that the total ticket sales amount to $765. The cost of each general admission ticket is $10, so the revenue from general admission tickets will be 10x. The cost of each youth ticket is $5, so the revenue from youth tickets will be 5y. Therefore, our second equation is:
10x + 5y = 765 ----(2)
Now, we can use these two equations to solve for the values of x and y.
To make the equation simpler, we can multiply equation (1) by 5 to eliminate the y variable:
5x + 5y = 485 ----(3)
Now, we can subtract equation (3) from equation (2):
(10x + 5y) - (5x + 5y) = 765 - 485
5x = 280
Dividing both sides of the equation by 5, we get:
x = 56
Now, substituting the value of x back into equation (1), we can solve for y:
56 + y = 97
y = 97 - 56
y = 41
Therefore, the ice rink sold 56 general admission tickets and 41 youth tickets.