Question

If 90 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $3.25, and the total receipts for the concert were $312, how many of each went to the concert?

Answer 1

To solve this problem, set up a system of equations to represent the number of adult and children's tickets, and the total receipts. Solve the system to find that there were 78 adult tickets and 12 children's tickets sold.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's call the number of adult tickets 'A' and the number of children's tickets 'C'. We know that the total number of tickets sold is 90, so we have the equation A + C = 90. We also know that the total receipts from the concert were $312, so we can write the equation 3.75A + 3.25C = 312.

Now we can solve this system of equations. Multiply the first equation by 3.25 and subtract it from the second equation to eliminate C:

3.75A - 3.25A + 3.25C - 3.25C = 312 - 3.25(90)

Simplifying, we get:

0.5A = 39

Divide both sides by 0.5 to solve for A:

A = 78

Substitute the value of A back into the first equation to solve for C:

78 + C = 90

C = 12

So, there were 78 adult tickets and 12 children's tickets sold at the concert.