Posted by **Robin** on Wednesday, November 7, 2012 at 11:48pm.

Andrea sells tickets at the Showtime Cinema. On Thursday night, Back to the Future was playing. Adults, senior citizens and children bought tickets at the following rates:

Adults $5.00

Senior Citizens $1.00

Children $.10

Andrea sold 100 tickets worth $100. How many adult, senior and children tickets were sold?

- Math -
**Reiny**, Thursday, November 8, 2012 at 8:56am
number of adults --- x

number of seniors --- y

number of children 100-x-y

5x + y + .1(100-x-x-y) = 100

times 10

50x + 10y + 100 -x-y = 1000

49x + 9y = 900

We are looking for integer solutions of x and y, (can't have partial people)

the x-intercept is appr 19

the y-intercept is appr 90

49x = 900-9y

x = (900-9y)/49

so 900-9y must be a multiple of 49

starting with trials of y = 1, 2, 3, ..

I lucked out at y = 2

when y = 2

x = 18

knowing the slope of our linear equation is -49/9

increasing the y value by 49 and decreasing the x by 9 would give us another solution.

so y = 51 and x = 9 would be another solution

so case 1:

18 adults

2 seniors

80 children

check:

-- sum is 100,

-- income = 5(18) + 1(2) + .1(80) = $100

case 2:

9 adults

51 seniors

40 children

check:

--- sum is 100

-- income = 5(9) + 1(51) + .1(40) = 100

(there is a third case of

0 adults

100 students

0 children , but it said that adults, seniors and children bought tickets , so I would exclude that)

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