Question

At a spring concert, tickets for adults cost $4.00 and tickets for students cost $2.50. How many of each kind of tickets were purchase if 125 tickets were bought for $413.00?

Answer 1

Using a system of linear equations, we determine that 67 adult tickets and 58 student tickets were purchased for the spring concert, based on the total number of tickets sold and the total amount collected.

Step-by-step explanation:

To solve the problem of determining how many adult and student tickets were purchased for the spring concert, we need to set up a system of linear equations. Let the number of adult tickets be A and the number of student tickets be S. We are given:

1. The total number of tickets sold was 125, so A + S = 125.
2. The total amount of money collected was $413, so 4.00A + 2.50S = 413.

Now we can solve this system using either substitution or elimination.

Step 1: Express one variable in terms of the other

A = 125 - S

Step 2: Substitute into the second equation

4.00(125 - S) + 2.50S = 413

Step 3: Simplify and solve for S

500 - 4S + 2.5S = 413
500 - 1.5S = 413
S = (500 - 413) / 1.5
S = 87 / 1.5
S = 58

Step 4: Solve for A using the number of student tickets

A = 125 - 58
A = 67

Therefore, 67 adult tickets and 58 student tickets were purchased for the spring concert.