Valencia Theater sold 499 tickets for a play. Tickets cost $14 per student with valid Valencia identification and $23 per none student. If total receipts were $8138, how many Valencia student tickets and none student tickets were sold?

pobi1k

pobi1k

Answered question

2022-09-09

Valencia Theater sold 499 tickets for a play. Tickets cost $14 per student with valid Valencia identification and $23 per none student. If total receipts were $8138, how many Valencia student tickets and none student tickets were sold?

Answer & Explanation

buciumau5r

buciumau5r

Beginner2022-09-10Added 8 answers

V tickets cost $14
N tickets cost $23

499 tickets cost $8138
Using the pricing, we can say: 14 V + 23 N = 8138 (1)

V tickets plus N tickets = total tickets =499
V + N = 499 ( 2 )
Solve for V: V = 499 - N

Sub that into (1): 14 ( 499 - N ) + 23 N = 8138

14 ( 499 - N ) + 23 N = 8138

- 14 N + 23 N = - 7000 + 14 + 8138

9 N = 1152

N = 128

Solve (2) for N: N = 499 - V

Sub that into (1): 14 V + 23 ( 499 - V ) = 8138

14 V - 23 V = - 23 ( 499 ) + 8138

- 9 V = - 11477 + 8138 = - 3339

V = 371

To check: V + N = 499

371 + 128 = 499

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