How many of each type of ticket must she sell?

Question

A concert promoter must sell 1000 tickets. She can sell premium tickets for $20 each, and discount tickets for $5 each. The total amount of money brought in from the sale of the tickets must be $14000. How many of each type of ticket must she sell? 

Answer 1

p + d = 1000

20p + 5d = 14,000

p = 1000 - d (or d = 1000 - p)

Suuuuuubstitute!

20(1000 - d) + 5d = 14,000

20,000 - 20d + 5d = 14,000

-15d = -6000

d = 400 discount tix

p = 1000 - 400

p = 600 discount tix