Mixture problem

Question

Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $30 and same-day tickets cost $40, For one performance, there were 65 tickets sold in all, and the total amount paid for them was $2300. How many tickets of each type were sold?

Answer 1

Let x be the number of $30 tickets sold and y be the number of $40 tickets sold:

1. there were 65 tickets sold in all: x + y = 65
2. total amount paid for them was $2300: 30x + 40y = 2300

x + y = 65

30x + 40y = 2300

From the first equation, y = 65 - x. Substitute into the second equation:

30x + 40y = 2300

30x + 40(65-x) = 2300

Solve for x, the number of $30 tickets sold. Once you have x, y = 65 - x.