Question

A movie theater has a seating capacity of 323. 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 $ 2354, How many children, students, and adults attended?

Answer 1

there are 186 children, 93 adults and 44 students.

Explanation:

there are 323 seats;

there is 2 children for 1 adult. rather the ratio between children and adults is 2:1

we can take the number of students to be y;

if we take the number of adults to be x then number of children will be 2x.

so in genral
`(323 - y)/(3) = x`

this means if you substract the number of students then you are left with only children and adults and we know the are x and 2x that is 3x. so if we divide 323-y by 3 we get x or rather the number of adults.

another inequality;

2354$ -7$*y = 12x+10x

we know the price for a student is 7$ so if we minus that from the total we get the total ticket price from only adults and childrens.

we know if there are x adults then the total adult ticket price is 12x. we know there are twice the number of adults, so the total ticket price for children is 5x*2 or 10x. this is the above inequality.

we have now two equations;

`(323-y)/(3) = x\\\\2354 - 7y = 22x`

we change the form of 1st one.

323-y = 3x

now multiply 7 on both sides we get'

2261 -7y = 21x

if we substract this from the second equation we can find theh value of x. which will be 93.

number of adults = 93, number of children = 93x3 =186 and put the value of x in one of the equation to find y, which is 44.