Question 84317: .5c + 5a + 3s = 100
c + a + s = 100
There is a fair where childs tickets cost $0.50 and adults tickets cost $5.00 each and senior citizens tickets cost $3.00. The total amount of tickets sold adds up to be $100.00. The total number of tickets sold is 100 also. How many children, adults, and seniors went to the fair?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! .5c + 5a + 3s = 100
c + a + s = 100
There is a fair where childs tickets cost $0.50 and adults tickets cost $5.00 each and senior citizens tickets cost $3.00. The total amount of tickets sold adds up to be $100.00. The total number of tickets sold is 100 also. How many children, adults, and seniors went to the fair?
:
multiply the 1st equation by 2 and subtract the 2nd equation from it:
1c + 10a + 6s = 200
1c + 1a + 1s = 100
--------------------subtraction eliminates c
0c + 9a + 5s = 100
5s = 100 - 9a
s = 100/5 - 9a/5
s = 20 - 9a/5
:
We know that both s and a have to be integers, this narrows the value of "a" down to a multiply of 5. Start with a = 5 and see what we have:
:
s = 20 - (9*5)/5
s = 20 - 45/5
s = 20 - 9
s = 11 seniors and
a = 5 adults
:
Find c:
c + 5 + 11 = 100
c = 100 - 16
c = 84 children:
:
Check all 3 solutions in the 2nd equation:
.5(84) + 5(5) + 3(11) =
42 + 25 + 33 = 100
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