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?

280 adult tickets

130 student tickets

190 children tickets

were sold at the concert

Step-by-step 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

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