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

Answer:

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#