MATH SOLVE

7 months ago

Q:
# 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.

Accepted Solution

A:

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! :)

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! :)