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?
First complete the equations below, where A
stands for Adults and S stands for Students.
2A + 0.75S = 1,109; A + S = 937
Now use the equations to find the number of
students and adults.
Students = [?]; Adults = []

Answer 1

Answer:

612 students and 325 adults

Step-by-step explanation:

I'll use substitution for this set of equations. I'll start with 2a + 0.75s = 1,109.

2a + 0.75s = 1,109

Subtract 0.75s from both sides.

2a = -0.75s + 1109

Divide both sides by 2.

a = 1/2(-3/4s + 1109)

Make 1/2(-3/4s + 1109) into a single fraction

a = -3/8s + 1109/2

Substitute -3/8s + 1109/2 for a in the other equation (a + s = 937).

-3/8s + 1109/2 + s = 937

Add -3/8s to s.

5/8s + 1109/2 = 937

Subtract 1109/2 from both sides.

5/8s = 765/2

Multiply both sides by 8/5, the reciprocal of 5/8.

s = 612

Now head back to the original equation, and substitute s for 612.

a = -3/8 * 612 + 1109/2

Multiply -3/8 by 612.

a = (-459 + 1109)/2

Add 1109 to -459 and divide by 2.

a = 650/2

a = 325

The system is solved. There are 612 students and 325 adults.