Question

8. The talent show committee sold a total of 530 tickets in advance. Student

tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were
$1740, how many of each type of ticket were sold?

... please solve this using systems of equations

Answer 1

Number of students tickets sold = x = 380 tickets

Number of adults tickets sold = y = 150 tickets

Explanation:

Let

Number of students tickets sold = x

Number of adults tickets sold = y

x + y = 530 (1)

3x + 4y = 1740 (2)

From (1)

x = 530 - y

Substitute x = 530 - y into (2)

3x + 4y = 1740

3(530 - y) + 4y = 1740

1590 - 3y + 4y = 1740

- 3y + 4y = 1740 - 1590

y = 150

Substitute y = 150 into (1)

x + y = 530

x + 150 = 530

x = 530 - 150

x = 380

Number of students tickets sold = x = 380 tickets

Number of adults tickets sold = y = 150 tickets