Question

Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost 25$ and same-day tickets cost 20$ . For one performance, there were 50 tickets sold in all, and the total amount paid for them was 1150$ . How many tickets of each type were sold?

Answer 1

Number of advance tickets sold = 30

Number of same-day tickets sold = 20

Explanation:

Let,

x be the number of advance tickets sold

y be the number of same-day tickets sold

According to given statement;

x + y = 50 Eqn 1

25x + 20y = 1150 Eqn 2

Multiplying Eqn 1 by 25

25(x+y=50)

25x + 25y = 1250 Eqn 3

Subtracting Eqn 2 from Eqn 3

(25x+25y)-(25x+20y) = 1250 - 1150

25x + 25y - 25x - 20y = 100

5y = 100

Dividing both sides by 5

`(5y)/(5)=(100)/(5)\\y=20`

Putting y = 20 in Eqn 1

x + 20 = 50

x = 50 - 20

x = 30

Hence,

Number of advance tickets sold = 30

Number of same-day tickets sold = 20