Question

If 112 people attend a concert and tickets for adults cost $2 while tickets for children cost $1.75 and total receipts for the concert was $207.25, how many of each went to the concert?

Answer 1

By setting up a system of equations and using the elimination method, it's determined that 45 adults and 67 children attended the concert.

Step-by-step explanation:

To solve how many adults and children attended the concert, we can use a system of equations with two variables representing the number of adults and children. Let's denote the number of adults as a and the number of children as c. We are given that the total number of people is 112, so:

a + c = 112 (Equation 1)

We also know that the total amount of money from ticket sales is $207.25, with adult tickets costing $2 and children's tickets costing $1.75. So, we have:

2a + 1.75c = 207.25 (Equation 2)

Now we have a system of two equations with two variables. We can solve these equations using substitution or elimination. For simplicity, we'll use the elimination method. Multiply both sides of Equation 1 by -1.75 to eliminate c:

-1.75a - 1.75c = -196

Adding this equation to Equation 2:

0.25a = 11.25

Divide both sides by 0.25 to find the number of adults:

a = 45

Substitute a with 45 in Equation 1 to find the number of children:

c = 112 - 45 = 67

Therefore, there were 45 adults and 67 children at the concert.