Question

If 159 people attend a concert and tickets for adults cost $3.5 while tickets for children cost $3 and total receipts for the concert was $517, how many of each went to the concert?

A) 120 adults, 39 children
B) 110 adults, 49 children
C) 100 adults, 59 children
D) 90 adults, 69 children

Answer 1

To solve for the number of adults and children who attended the concert, we formed a system of two equations based on the given information. By solving these equations, it was determined that there were 80 adults and 79 children at the concert.

Step-by-step explanation:

To answer how many adults and children went to the concert given that 159 people attended, adult tickets cost $3.5, children's tickets cost $3, and total receipts for the concert were $517, we need to set up a system of equations and solve for the number of adult and child ticket holders.

Let's define the following variables:

• A = number of adults
• C = number of children

Based on the information given, we can form two equations:

1. A + C = 159 (the total number of people attending)
2. 3.5A + 3C = $517 (total receipts from ticket sales)

Now, let's solve the system of equations:

1. Multiply the first equation by 3 to eliminate the C variable: 3A + 3C = 477
2. Subtract this new equation from the second equation:
   3.5A + 3C = $517
   -
   3A + 3C = 477
   _____________________
   0.5A = $40
3. Divide both sides by 0.5 to find A:
   A = 80
4. Substitute A back into the first equation:
   A + C = 159
   80 + C = 159
   C = 159 - 80
   C = 79

Therefore, there were 80 adults and 79 children attending the concert.