Question

Trevon’s school is selling tickets to a fall musical. On the first day of ticket sales the school sold 13 adult tickets and 12 student tickets for a total of $211. The school took in $65 on the second day by selling 5 adult tickets and 3 student tickets. What is the price of one adult ticket and one student ticket?
Write two separate equations and what is the price of one adult ticket and one student ticket.

Answer 1

9514 1404 393

Answer:

• adult: $7
• student: $10

Step-by-step explanation:

Let a and s represent the prices of adult and student tickets, respectively.

  13a +12s = 211 . . . . . . ticket sales the first day

  5a +3s = 65 . . . . . . . ticket sales the second day

Subtracting the first equation from 4 times the second gives ...

  4(5a +3s) -(13a +12s) = 4(65) -(211)

  7a = 49 . . . . . . . simplify

  a = 7 . . . . . . . divide by 7

  5(7) +3s = 65 . . . . substitute into the second equation

  3s = 30 . . . . . . . subtract 35

  s = 10 . . . . . . . divide by 3

The price of one adult ticket is $7; the price of one student ticket is $10.