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

Explanation:

Let's define the variables: Let x be the number of adult tickets sold. Let y be the number of child tickets sold. We can now set up a system of equations based on the given information: 1. The total number of tickets sold is 210: x + y = 210 2. The total revenue generated is $671.10: 4.75x + 2.10y = 671.10 To solve this system of equations, we can use the substitution or elimination method. Let's solve using the elimination method: Multiply the first equation by 2.10 to eliminate y: 2.10x + 2.10y = 441.00 Now, subtract the second equation from this modified first equation: (2.10x + 2.10y) - (4.75x + 2.10y) = 441.00 - 671.10 Simplifying the equation: 2.10x - 4.75x = -230.10 -2.65x = -230.10 Divide both sides by -2.65: x = 86.792 Since we cannot have a fraction of a ticket, we can round x to the nearest whole number: x ≈ 87 Substitute the value of x back into the first equation to find y: 87 + y = 210 y = 210 - 87 y = 123 Therefore, approximately 87 adult tickets and 123 child tickets were sold.