A movie theater has a seating capacity of 195. 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 $ 1404, How many children, students, and adults attended? 

 

 ____   children attended.

  ______  students attended. 

  _____  adults attended. 

Given

Total capacity=195

There are half as many adults as there are children

Let the number of children = 2x

Then number of adults = half of 2x = x

Since the total capacity is 195, if the theatre is fully occupied, then number of students = 195-(Number of adults + number of children

Number of students=195-(2x+x)=195-3x

The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults.

the total ticket sales was $ 1404

So we can write

1404=5*number of children+7*number of students+12*number of adults

1404=5*2x+7*(195-3x)+12*x

1404=10x+1365-21x+12x

1404=x+1365

x=1404-1365=39

We take number of children as 2x

So number of children = 2*39 = 78

Number of adults = x = 39

Number of students = 195-3x = 195-3*39 = 78