Question

A movie theater has a seating capacity of 343. 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 $
2486, How many children, students, and adults attended?
children attended.
students attended.
adults attended.

Answer 1

Answer:

170 children, 88 students, 85 adults

Step-by-step explanation:

x = children

y = students

z = adults

x + y + z = 343

5x + 7y + 12z= 2486

z = 1/2x

you can solve by elimination or substitution or both.

3 equations with 3 unknowns

Answer 2

By solving a system of equations, we conclude that:

• 134 children.
• 142 students
• 67 adults.

How many children, students, and adults attended?

Let's define the variables:

• C = number of children.
• S = number of students.
• A = number of adults.

We know that the theater has a capacity of 343, then:

C + S + A = 343

We also know that there are half as many adults as there are children, then:

A = C/2

Finally, we know that the total profit is $2,468, then:

C*$5,00 + S*$7.00 + A*$12.00 = $2,468

So we have a system of 3 equations:

C + S + A = 343

A = C/2

C*$5,00 + S*$7.00 + A*$12.00 = $2,468

First, we can replace the second equation into the other two to get:

C + S + C/2 = 343

C*$5,00 + S*$7.00 + (C/2)*$12.00 = $2,468

Now we can rewrite the first equation as:

S = 343 - (3/2)*C

Now we can replace that on the first equation:

C*$5,00 + (343 - (3/2)*C)*$7.00 + (C/2)*$12.00 = $2,468

$2,401 + C*$0.50 = $2,468

C = ($2,468 - $2,401)/$0.50 = 134

And we know that:

A = C/2 = 134/2 = 67

And:

S =  343 - (3/2)*C =  343 - (3/2)*134 = 142

Then there are:

• 134 children.
• 142 students
• 67 adults.

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

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