SOLUTION: If you spend $100 on 100animals (8hens=$1, 1sheep=$1 and cows cost $10) and you must buy one of each, how many of each do you buy?

Question 344196: If you spend $100 on 100animals (8hens=$1, 1sheep=$1 and cows cost $10) and you must buy one of each, how many of each do you buy?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You can't buy 100 cows, because 100 x $10 = $1,000
50 cows is still too much, since 50 x $10 = $500
since 10 cows cost 10 x $10 = $100, you must spend less than that
Suppose you buy 9 cows, then 9 x $10 = $90
There is $10 left
If you bought all hens to get 100 animals, that would make
80 hens = 80 x 1/8 = $10, and $90 + $10 = $100, but
there are only 9 + 80 = 89 animals
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Suppose you buy 8 cows, then 8 x $10 = $80
then 160 hens = 160 x 1/8 = $20, that's 168 animals
If you buy 72 hens, then 72 x 1/8 = $9
There is $11 left to buy 11 sheep, but 8 + 72 + 11 = 91
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If you buy 8 cows and 80 hens, that's 80 x 1/8 = $10
$10 + $80 = $90 , you have $10 to buy 10 sheep, and that's
8 + 80 + 10 = 98 animals
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If you buy 8 cows and 88 hens that's 88 x 1/8 = $11
$11 + $80 = $91 You have $9 left to buy 9 sheep, and that's
8 + 88 + 9 = 105 animals
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It looks like you can't do it with 8 cows, and I'd guess that
7 cows would work
7 cows = $70
80 hens = $10
13 sheep = $13
$70 + $10 + $13 = $93
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7 cows = $70
72 hens = $9
21 sheep = $21
$70 + $9 + $21 = $100
That's 100 animals for $100

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