Question

a school purchased 72 tickets for a field trip to the theater. adult tickets cost $15 and student tickets cost $10. the school spent $760 on tickets. how many adult and student tickets did the school purchase? solve the system using elimination. enter the answer. keyboard help

Explanation:

Step1: Define variables and set up equations

Let \( x \) be the number of adult tickets and \( y \) be the number of student tickets. We have two equations:

1. \( x + y = 72 \) (total number of tickets)
2. \( 15x + 10y = 760 \) (total cost of tickets)

Step2: Eliminate one variable

Multiply the first equation by 10: \( 10x + 10y = 720 \)
Subtract this from the second equation:
\( (15x + 10y) - (10x + 10y) = 760 - 720 \)
\( 5x = 40 \)

Step3: Solve for \( x \)

Divide both sides by 5: \( x = \frac{40}{5} = 8 \)

Step4: Solve for \( y \)

Substitute \( x = 8 \) into \( x + y = 72 \):
\( 8 + y = 72 \)
\( y = 72 - 8 = 64 \)

Answer:

The school purchased 8 adult tickets and 64 student tickets.