A movie theater has a seating capacity of 329. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2388, How many children, students, and adults attended? ___ children attended.
___students attended.
adults attended.

170 children

74 students

85 adults

Step-by-step explanation:

Given

Let:

For the capacity, we have:

For the tickets sold, we have:

Half as many as adults are children implies that:

Required

Solve for A, C and S

The equations to solve are:

-- (1)

-- (2)

-- (3)

Make C the subject in (3)

Substitute in (1) and (2)

-- (1)

Make S the subject

-- (2)

Substitute

Solve for A

Recall that:

Recall that:

Hence, the result is:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

2: 10

step-by-step explanation: