Question

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?

Answer 1

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`