SOLUTION: A rancher buys 100 live animals for $100. Chickens cost 50cents each, goats cost $3.50 and cows $10.00 each. How many of each did the rancher buy? Is more than one combination poss

Question 241567: A rancher buys 100 live animals for $100. Chickens cost 50cents each, goats cost $3.50 and cows $10.00 each. How many of each did the rancher buy? Is more than one combination possible?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rancher buys 100 live animals for $100.
Chickens cost 50 cents each, goats cost $3.50 and cows $10.00 each.
How many of each did the rancher buy? Is more than one combination possible?
:
Write two equations:
:
No. of animals
ch + g + c = 100
:
Cost equation
.5ch + 3.5g + 10c = 100
:
Two equations, 3 unknowns
We know there can't be very many cows
After trying a couple values for no. of cows, came up with 4 cows,
they're worth $40, our two equations then are:
:
ch + g = 100 - 4
ch + g = 96
and
.5ch + 3.5g = 100 - 40
.5ch + 3.5g = 60
:
Multiply the 2nd equation by 2 and subtract the 1st equation:
ch + 7g = 120
ch + g = 96
---------------- subtracting eliminates ch
0 + 6g = 24
g =
4 goats
:
Find chicks
ch + 4 = 96
ch = 96 - 4
92 chickens
:
We have then: 4 cows, 4 goats, 92 chickens
;
;
Check in the cost equation
.5(92) + 3.5(4) + 10(4) =
46 + 14 + 40 = 100
Not sure if this is the only solution. You can try other values for no. of cows and see.
I don't think odd number of cows will work
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