# math

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you have to buy 100 animals. roosters cost 5.00, hens cost 1.00 and chicks cost .05cents. how many of each animal can I buy?

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You left out the amount of money you have to spend.

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sorry 100.00

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You left out the cost of the purchases, typically \$100.

Here is a similar version of this oldie.
If you had a \$100.00 to spend and need to buy a 100 animals, and cows cost
\$10.00, pigs \$3.00, chichens .50 cents each,.how many of each can you buy?

Let C, P, and F be the numbers of cows, pigs, and fowl.
1--C + P + F = 100
2--10C + 3P + .5F = 100 or 100C + 30P + 5F = 1000
3--Multiplying (1) by 5 and subtracting from (2) yields 19C + 5P = 100
4--Dividing through by 5 gives P + 3C + 4C/5 = 20
5--4C/5 must be an integer as must be C/5
6--Let C/5 = k making C = 5k
7--Substituting (6) back into (3) gives 95k + 5P = 100 making P = 20 - 19k
8--k can only be 1 making C = 5, P = 1, and F = 94
Check: 10(5) + 3(1) + .5(94) = \$100

Alternatively

Let C, P, and F be the numbers of cows, pigs, and fowl.
1--C + P + F = 100
2--10C + 3P + .5F = 100 or 100C + 30P + 5F = 1000
3--Multiplying (1) by 5 and subtracting from (2) yields 19C + 5P = 100
4--Solving for P, P = 20 - 19C/5
5--19C/5 must be an integer meaning that C must be evenly divisible by 5.
6--Thus, C must be 5 making P = 1, C = 5, and F = 94.

I'll let you work it out with your numbers.

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