Question

A school fund raising event sold a total of 210 tickets and generated a total revenue of $671.10. There are two types of tickets: adult tickets and child tickets. Each adult ticket costs $4.75, and each child ticket costs $2.10. Write and solve a system of equations to answer the following questions.

Answer 1

To solve the problem of how many adult and child tickets were sold during a school fundraising event, we set up a system of equations considering the total number of tickets and the total revenue. The solution to the system of equations is that 86 adult tickets and 124 child tickets were sold.

Step-by-step explanation:

The school fundraising event problem can be solved with a system of equations. Let's denote the number of adult tickets as A and the number of child tickets as C. We know that the total number of tickets sold is 210, and the total revenue is $671.10, with adult tickets costing $4.75 each and child tickets $2.10 each.

We can then write the following equations based on the information given:

1. A + C = 210 (the total number of tickets sold)
2. 4.75A + 2.10C = 671.10 (the total revenue generated)

To solve this system, manipulate the first equation to get a value for one variable in terms of the other. Subtract the equation for C from the total tickets:

A = 210 - C

Now, substitute this value into the second equation:

4.75(210 - C) + 2.10C = 671.10

Solve for C:

4.75(210) - 4.75C + 2.10C = 671.10

999.75 - 2.65C = 671.10

2.65C = 999.75 - 671.10

2.65C = 328.65

C = 124

Now, substitute C back into the first equation to find A:

A = 210 - 124 = 86

So, the number of adult tickets sold is 86 and the number of child tickets sold is 124.