Question

A movie theatre Has a seating capacity of 165. The theater charges five dollars for children seven dollars for students and $12 for adults. There are half as many adults as there are children. If the total ticket sales was $1182 how many children students and adults attended?

Answer 1

Answer:

The number of children are 54, number of students are 84 and number of adults are 27.

Step-by-step explanation:

Let the number of children be $x$

Let the number of students be $y$

Let the number of adults be $z$

As per question,

$x+y+z=165\\5x+7y+12z=1182$

Now, adults are half of the children.

So, $z=\frac{x}{2}\\x=2z$

Now, plug in $x=2z$ in the first two equations.

$2z+y+z=165\\3z+y=165-----------------3\\\\ 5(2z)+7y+12z=1182\\10z+12z+7y=1182\\7y+22z=1182 ---------------- 4$

Multiply equation (3) by -7 and add it to equation (4).

$(3z+y=165)\times -7=-21z-7y=-1155\\\\-21z-7y+7y+22z=-1155+1182\\(22z-21z)+(7y-7y)=27\\z=27$

Solve for the remaining variables.

$x=2z=2\times 27=54$

$x+y+z=165\\54+y+27=165\\81+y=165\\y=165-81=84$

Therefore, the number of children are 54, number of students are 84 and number of adults are 27.