Cinema Word Problem

Let

X the number of people who paid regular-priced tickets

Y the number of students

41-x-y number of students and people who paid regular-priced tickets

400 12x 9y 41-x-y

400-41 11x 8y

359 11x 8y

X 10 20 30

Y 31 1 /8 17 3 /8 3 5 /8 8y 359-11x

Y (359-11x /8

Y (359-110 /8

Y 249 /8

Y 31 1 /8

Y (359-220 /8

Y 139 /8

Y 17 3 /8

Y (359-330 /8

Y 29 /8

Y

3 5 /8

With this solution , there are a lot of possible solutions which are the points where the line passes through . However , it is impossible to have a 3 /8 of a person entering the cinema . Then , that would be scary . We could identify possible solutions here but it would be hard to examine and select those points where x and y holds a whole number

However , we know that if there was no discount , then the accumulated bill would have been 492 SF . To get the subtract 400 from 492 , which is equal to 92

Using the formula

Amount of discount Accumulated bill without discount-Final bill

Amount of discount 41 people (12 SF )-400

Amount of discount 492-400

Amount of discount 92

Adopting the same , amount of discount for the students

Amount of discount Regular Price-Price for Students

Amount of discount 12-9

Amount of discount for students 3 SF

Adopting the same , amount of discount for the children

Amount of discount Regular Price-Price for children

Amount of discount 12-1

Amount of discount 11

Now that we know the amount that each group gets (3SF for students and 11 SF for children ) and the multiples of each group which is less than 92 From the multiples of 3SF (students ) and 11 SF (children , we would notice that by adding numbers for every 11th interval going down for the multiples of 3 and numbers for every 3rd interval going up from 77 for the multiples of 11 , we are able to get the sum of 92 . We can not go any further than this because it will cause a negative number to appear

Such that

81 SF 11 SF 92

48 SF 44 SF 92

15 SF 77 SF 92

Now that we know the could now divide it by the individual discount for a person belonging to that group , such that

A Amount of discount taken by group

B Amount of discount for each member of that group

C Number of people in that group

Then

A /B C

Now , we can identify the number of persons in each group for the three possible answers above using the formula A /B C

81 SF /3 SF 27 Students 11 SF / 11 SF 1 Child

48 SF /3 SF 16 Students 44 SF /11 SF 4 children

15 SF /3 SF 5 Students 77 SF / 11 SF 7 children

These three are the only possible answers that would yield a positive result for the number of children and number...