Question

A total of 937 people attended the play admission was $2.00 for adults and $0.75 for students. The total ticket sales amounted to $1,109. How many students and adults attended the school play?

Answer 1

612 students attended and 325 adults attended the play

Solution:

Let "s" be the number of students attended the play

Let "a" be the number of adults attended the play

Cost of 1 adult ticket = $ 2

Cost of 1 student ticket = $ 0.75

Given that total 937 people attended the play

number of students + number of adults = 937

s + a = 937 ---------- eqn 1

The total ticket sales amounted to $1,109

number of adults x Cost of 1 adult ticket + number of students x Cost of 1 student ticket = 1109

$a \times 2 + s \times 0.75 = 1109$

2a + 0.75s = 1109 ---- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

s = 937 - a -------- eqn 3

Substitute eqn 3 in eqn 2

2a + 0.75(937 - a) = 1109

2a + 702.75 - 0.75a = 1109

1.25a = 1109 - 702.75

1.25a = 406.25

$a = \frac{406.25}{1.25}$

a = 325

From eqn 3,

s = 937 - 325

s = 612

Thus 612 students attended and 325 adults attended the play