# 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? ##### 1 Answer Oct 26, 2017 There were $371$Valencia tickets and $128$Non-student sold. #### Explanation: V tickets cost $14
N tickets cost $23 499 tickets cost $8138
Using the pricing, we can say: $14 V + 23 N = 8138 \to$ $\left(1\right)$

V tickets plus N tickets = total tickets $= 499$
$V + N = 499 \to$ $\left(2\right)$
Solve for V: $V = 499 - N$

Sub that into $\left(1\right)$: $14 \left(499 - N\right) + 23 N = 8138$

$14 \left(499 - N\right) + 23 N = 8138$

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

$9 N = 1152$

$N = 128$

Solve $\left(2\right)$ for N: $N = 499 - V$

Sub that into $\left(1\right)$: $14 V + 23 \left(499 - V\right) = 8138$

$14 V - 23 V = - 23 \left(499\right) + 8138$

$- 9 V = - 11477 + 8138 = - 3339$

$V = 371$

To check: $V + N = 499$

$371 + 128 = 499$