Answer:
Number of adults = 350
Number of students = 200
Number of Children under 12 = 50
Step-by-step 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
