Question

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 1

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: `14V+23N=8138to` `(1)`

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

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

`14(499-N)+23N=8138`

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

`9N=1152`

`N=128`

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

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

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

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

`V=371`

To check: `V+N=499`

`371+128=499`