Math
posted by Robin on .
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?

number of adults  x
number of seniors  y
number of children 100xy
5x + y + .1(100xxy) = 100
times 10
50x + 10y + 100 xy = 1000
49x + 9y = 900
We are looking for integer solutions of x and y, (can't have partial people)
the xintercept is appr 19
the yintercept is appr 90
49x = 9009y
x = (9009y)/49
so 9009y 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)