Question

A jazz concert brought in $207,000 on the sale of 8,100 tickets. If the tickets sold for $20 and $30 each, how many of each type of ticket were sold?

Answer 1

x = 20 dollar tickets and y = 30 dollar tickets

x + y = 8100.....x = 8100 - y
20x + 30y = 207,000

20(8100 - y) + 30y = 207,000
162,000 - 20y + 30y = 207,000
-20y + 30y = 207,000 - 162,000
10y = 45,000
y = 45,000/10
y = 4500 <=== there were 4500 thirty dollar tickets sold

x + y = 8100
x + 4500 = 8100
x = 8100 - 4500
x = 3600 <=== there were 3600 twenty dollar tickets sold