Question

A school band performs a spring concert for a crowd of 600 people The revenue for the concert is $3150. There are 150 more adults at the concert than students. Students- $3 Adults- $7 Children under 12- $2

How many of each type ticket are sold?

Answer 1

Number of adults = 350

Number of students = 200

Number of Children under 12 = 50

Explanation:

Let

Number of adults = x

Number of students = y

Number of Children under 12 = z

Cost of each ticket

Students = $3

Adults = $7

Children under 12 = $2

Total crowd at the concert = 600

Total revenue = $3,150

There are 150 more adults at the concert than students.

That is, adults = y + 150

The equations

x + y + z = 600

7x + 3y + 2z = 3,150

Recall,

x = y + 150

y + 150 + y + z = 600

7(y + 150) + 3y + 2z = 3,150

2y + z + 150 = 600

7y + 1050 + 3y + 2z = 3,150

2y + z = 600 - 150

10y + 2z = 3150 - 1050

2y + z = 450 (1)

10y + 2z = 2,100 (2)

Multiply (1) by 2

4y + 2z = 900 (3)

10y + 2z = 2,100 (2)

Subtract (3) from (2)

10y - 4y = 2100 - 900

6y = 1200

Divide both sides by 6

y = 1200/6

= 200

Substitute the value of y into (1)

2y + z = 450

2(200) + z = 450

400 + z = 450

z = 450 - 400

= 50

z = 50

Substitute value of y into

x = y + 150

x = 200 + 150

= 350

x = 350

Therefore,

Number of adults = 350

Number of students = 200

Number of Children under 12 = 50