Question

Ticket prices for Students ($3), Adults ($7), Children under 12 ($2) A School band performs a concert for a crowd of 600 people. The revenue for the concert is $3150. There are 150 more adults at the concert than students. How many of each type of ticket are sold?

Answer 1

280 adult tickets

130 student tickets

190 children tickets

were sold at the concert

Explanation:

Let the number of students be s , adults a and children c

Total 600;

Thus;

a + s + c = 600 •••••••(i)

let us look at revenue

Revenue = number * ticket price

For adults; a * 7 = $7a

For students ; s * $3 = $3s

For children; c * $2 = $2c

Total is 3150

thus;

7a + 3s + 2c = 3150 ••••••••(ii)

150 more adults than students;

a = s + 150 ••••••(iii)

Substitute iii into ii and i

into ii

7(s + 150) + 3s + 2c = 3150

7s + 1050 + 3s + 2c = 3150

9c + 3s = 3150-1050

9c + 3s = 2,100 •••••••(x)

Substitute into i

a + s + c = 600

s + 150 + s + c = 600

2s + c = 600 - 150

2s + c = 450

c = 450 - 2s ••••••(xx)

Now substitute xx into x

9(450-2s) + 3s = 2100

= 4050-18s + 3s = 2100

4050-2100 = 18s - 3s

15s = 1950

s = 1950/15

s = 130

c = 450 -2s

c = 450 - 2(130)

c = 450 - 260

c = 190

a = 150 + s

a = 150 + 130

a = 280