The booster club sold tickets to a high school basketball game. They sold 700 student tickets and 500 general admission tickets, and raised a total of $5000. The combined cost of one student ticket and one general admission ticket was $8.
The equations and graph below can be used to determine how much each ticket type cost, where s represents the cost of one student ticket and g represents the cost of one general admission ticket.
Total ticket sales: 700s + 500g = $5000
Total cost for one student and one general admission ticket: s + g = 8
What was the price, in dollars, of a general admission ticket?
s = 8 - g
700s + 500g =5000
Substitute 8-g for s in second equation and solve for g. Insert that value into the first equation and solve for s. Check by inserting both values into the second equation.
To find the price of a general admission ticket, we can use the given equations.
Let's start by solving the second equation, which states that the total cost for one student and one general admission ticket is $8:
s + g = 8
Next, we can solve the first equation, which represents the total ticket sales:
700s + 500g = 5000
To solve this system of equations, we can use the method of substitution or elimination.
Let's use substitution. Solve the first equation for s:
s = 8 - g
Now, substitute this value of s into the second equation:
700(8 - g) + 500g = 5000
Simplify the equation:
5600 - 700g + 500g = 5000
Combine like terms:
800g = 5000 - 5600
800g = -600
Divide both sides by 800:
g = -600 / 800
g = -0.75
The price of a general admission ticket cannot be negative, so we made an error somewhere. Let's double-check our calculations.
We'll go back to the equation 700s + 500g = 5000 and substitute the value of s from the second equation:
700(8 - g) + 500g = 5000
Simplify the equation:
5600 - 700g + 500g = 5000
Combine like terms:
-200g = 5000 - 5600
-200g = -600
Divide both sides by -200:
g = -600 / -200
g = 3
The price of a general admission ticket is $3.