Three hundred people attended a band concert. Reserved seat tickets were sold at $100 each while general admission tickets cost $60 each. If the sales totaled $26000, how many tickets of each type were sold?

1 Answer
Sep 4, 2015

Answer:

200 tickets at $100
100 tickets at $60

Explanation:

Define variables
#color(white)("XXX")x#: number of $100 tickets
#color(white)("XXX")y#: number of $60 tickets

We are told
[1]#color(white)("XXXX")x+y = 300#
[2]#color(white)("XXXX")100x+60y = 26000#

Multiplying [1] by #60#
[3]#color(white)("XXXX")60x+60y=18000#

Subtracting [3] from [2]
[4]#color(white)("XXXX")40x = 8000#

Dividing both sides by #40#
[5]#color(white)("XXXX")x =200#

Substituting #200# for #x# in [1]
[6]#color(white)("XXXX")200 + y = 300#

Subtracting #200# from both sides
[7]#color(white)("XXXX")y=100#