Question 22497: I am having a problem setting up this word problem. Can someone please help me structure this word problem.
a man buys 100 birds for $100.00. a rooster is worth$10.00, hens are worth $3.00, and chicks are worth $1.00 a pair. how many roosters, hens, and chicks did he buy if he bought atleast one of each?
He bought 1 rooster, 1 hen and 2 chicks which is 14.00 worth, right? what am I missing?
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! But he bought 100 birds for $100! The roosters, hens, and chicks are all birds.
So we want a system of equations:
Let r=# of roosters, h=# of hens, and c=# of chickens.
Then r + h + c = 100 (from "100 birds") and
10r + 3h + 1(c/2) = 100 (from $100).
OK, then I substituted with c and got c=200-20r-6h, so r+h+200-20r-6h=100.
So 100=19r+5h.
Then h=(-19/5)r + 20, and since r, h, and c must be whole numbers, I wanted to make r a multiple of 5 (to cancel out the denominator in the coefficient). So, I tried r=5, and then solved for h and got h=-19+20=1, so both are whole numbers.
I then went back to the original equations and solved for c, and got c=94. I tested these values in both equations and they worked, so I knew the answer was successful:).
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