SOLUTION: A farmer buys 100 animals for $100.00. The animals include at least one cow, one pig, and one chicken, but no other kind. If a cow costs $5.00, a pig costs $1.00, and a chicken c

Question 707095: A farmer buys 100 animals for $100.00. The animals include at least one cow, one pig, and one chicken, but no other kind. If a cow costs $5.00, a pig costs $1.00, and a chicken costs $0.50, how many of each did he buy?
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
w cow ____________$5 each
p pig ____________$1 each
n chicken ________$0.50 each

w+p+n=100, farmer bought 100 animals
Examining the cost: 5*w+1*p+0.5*n=100, farmer spent 100 dollars

w>=1, p>=1, n>=1

By chance, I assumed w=k, just some assumed natural number, and solved the system for p and n. I only used simple algebra-1 stuff; no matrix operations.
Work was then done on system:
p+0.5n=100-5k
p+n=100-k

My initial results were w=k, p=100-9k, n=8k.
One of the specifications was that at least one animal of each kind was bought. I tried k=1 and computed what that would do for w, p, and n. Good results: if k=1, then w=1, p=91, and n=8. Total 100 animals.
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