Question

A school put on a music program. Adult tickets were sold for $8.00 each, and child tickets were sold for $4.00 each. The school collected $2,688.00 from ticket sales. If a total of 372 tickets were sold, how many were adult tickets and how many were child tickets?

Answer 1

To find the number of adult and child tickets sold, we can set up a system of equations based on the given information and solve for the variables. Using the method of substitution, we can find that there were 300 adult tickets and 72 child tickets sold.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's assign variables to represent the number of adult and child tickets. Let's say x represents the number of adult tickets and y represents the number of child tickets.

We can set up the following two equations based on the given information:

Equation 1: x + y = 372 (since the total number of tickets sold is 372)

Equation 2: 8x + 4y = 2688 (since the total amount collected from ticket sales is $2688)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From Equation 1, we can rewrite it as x = 372 - y. Substituting this value of x into Equation 2, we get:

8(372 - y) + 4y = 2688

2976 - 8y + 4y = 2688

-4y = 2688 - 2976

-4y = -288

y = -288 / -4

y = 72

Now we can substitute the value of y back into Equation 1 to find the value of x:

x + 72 = 372

x = 372 - 72

x = 300

Therefore, there were 300 adult tickets sold and 72 child tickets sold.