Question 93380
John bought 100 animals for $100. He bought more than 70 baby chicks. 8 @ 1$. a certain amount of goats that are $10 each and a certain amount of ducks that are $1 each.......how many of each animal did he buy??
:
Since the cost of the ducks and goat are even dollars, the total of the chicks
has to be even dollars also
:
70 chicks @ 8 for a dollar: 70/8 = $8.75 for the 70 chicks, or .125 apiece,
add two more, to make it an even dollar amt: 72/8 = $9 for chicks
:
That makes our equations to be:
72 + d + g = 100; no. of animals
d + g = 100 - 72
d + g = 28 
and 
9 + d + 10g = 100; cost of animals
d + 10g = 100 - 9
d + 10g = 91
:
Use the two above equations and subtract:
d + 10g = 91
d +  g  = 28
----------------subtracting eliminates d
9g = 63
g = 63/9
g = 7 goats
:
Find d using d + g = 28
d + 7 = 28
d = 28 -7
d = 21 ducks
:
We have 72 chicks, 21 ducks and 7 goats, adds up to 100 animals
:
Check using the $amt equation:
9 + 21 + 7(10) = $100
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Did this make sense?