Question

April sold 75 tickets to the school Christmas play and collected $495. If adult tickets cost $8 and children tickets were $5 how many adult and children tickets were sold.

Answer 1

40 adult tickets were sold and 35 children tickets were sold

Solution:

Let "a" be the number of adult tickets sold

Let "c" be the number of children tickets sold

Cost of 1 adult ticket = $ 8

Cost of 1 children ticket = $ 5

Given that April sold 75 tickets to the school Christmas play and collected $495

Number of tickets sold = 75

number of adult tickets sold + number of children tickets sold = 75

a + c = 75 ----- eqn 1

Given that April collected $495

Thus we can frame a equation as:

number of adult tickets sold x Cost of 1 adult ticket + number of children tickets sold x Cost of 1 children ticket = $ 495

$a \times 8 + c \times 5 = 495$

8a + 5c = 495 ----- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "a" and "c"

From eqn 1,

a = 75 - c ---- eqn 3

Substitute eqn 3 in eqn 2

8(75 - c) + 5c = 495

600 - 8c + 5c = 495

-3c = 495 - 600

-3c = - 105

c = 35

Substitute c = 35 in eqn 3

a = 75 - 35

a = 40

Thus 40 adult tickets were sold and 35 children tickets were sold