Question

The box office took in a total of $2905 in paid admissions for the high-school musical. Adult tickets cost $8 each, and student tickets cost $3 each. If 560 people attended the show, how many were students? Let s = the number of students attending, and let a = the number of adults attending. Which two equations can be used to solve this problem? Select the two that apply.

Answer 1

There are no equations to choose from but it should look like the following.

a= # of adult tickets
s= # of student tickets

QUANTITY EQUATION
a + s= 560

COST EQUATION
$8a + $3s= $2905

***If you have to also solve for the number of adults and students, here are the steps.

STEP 1:
multiply quantity equation by -8

-8(a + s)= -8(560)
-8a - 8s= -4480

STEP 2:
add cost equation and step 1 equation

$8a + $3s= $2905
-8a - 8s= -4480
a term cancels out to zero
-5s= -1575
divide both sides by -5
s= 315 students

STEP 3:
substitute s=315 in quantity equation
a + s= 560
a + 315= 560
subtract 315 from both sides
a= 245 adults

ANSWER:
Quantity Equation
a + s= 560

Cost Equation
$8a + $3s= $2905

Hope this helps! :)