Question 96100: A farmer buys 100 live animals for $100. How many of each doe she buy if chicks are .10 each, pigs are 42 and sheep are $5 each?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! I think there is typo here; pigs are not 42, I assume you meant pigs are $2
Let c = no. of chicks; p = no. of pigs; s = no. sheep
:
A farmer buys 100 live animals for $100.
No. of animals equation:
c + p + s = 100
:
How many of each does she buy if chicks are .10 each, pigs are 42 and sheep are $5 each?
the $$ equation:
.10c + 2p + 5s = 100
:
We have two equations but 3 unknowns, however,
We know there has to be a lot of chicks and the
number of chicks must equal a multiple of 10, like 60, 70, 80
:
Assume there are 70 chicks, they're worth $7, our two equations then:
:
p + s = 100 - 70
p + s = 30
and
2p + 5s = 100 - 7
2p + 5s = 93
:
Multiply the 1st equation by 2 and subtract it from the 2nd equation:
2p + 5s = 93
2p + 2s = 60
---------------- subtracting eliminates p
0p + 3s = 33
s = 33/3
s = 11 sheep
:
Find p
p + 11 = 30
p = 30 - 11
p = 19 pigs
:
c = 70 chicks (assumed)
:
Check using the $$ equation:
.10(70) + 2(19) + 5(11) =
7 + 38 + 55 = 100
:
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