SOLUTION: Tickets to a show cost $2 for kids, $3 for seniors, and $5 for adults. If there were twice as many kids as seniors, and if 91 tickets were sold and $311 was collected, how many of

Question 218143: Tickets to a show cost $2 for kids, $3 for seniors, and $5 for adults. If there were twice as many kids as seniors, and if 91 tickets were sold and $311 was collected, how many of each te of ticket was sold?
My class just started these kind of problems at school, and this is one of the example we have to do, and I don't understand it but I did similar problems as this.
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Let k=# kids tickets, s=#senior tickets,,,and a=# adult tickets
.
k+s+a=91,,,,but k=2s
.
2s +s +a =91
.
3s +a =91,,,,,or a = (91-3s)
.
$2*k + $3*s +$5*a =311
.
2*(2s) + 3*s +$5*(91-3s) =311,,,,,lots of substitutions
.
4s +3s -15s +455 =311
.
-8s = -144
.
s=18
.
subst back in,,,k=2s = 2*18 =36,,,,a= 91-3s=91-3*18= 37
.
Total # tickets = k+s+a=36+18+37=91,,,,,ok
.
checking $,,,2*36 +3*18 +5*37 = 72+54+185 = 311,,,,ok
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