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