10.00X + .5X + Y = 100

Question

You have a total of 100 cows, sheep, and goats. The cows cost $10 ea, sheep $3 ea, and goats $0.50 ea. And you only spend a total of $100. How many of each animal can you buy by spending exactly $100, no more or less?

Answer 1

C=number of cows, S=number of sheep, number of goats=100-(C+S).

Cost of animals: 10C+3S+0.5(100-C-S)=100,

10C+3S+50-0.5C-0.5S=100,

9.5C+2.5S=50, 19C+5S=100,

C=(100-5S)/19=(95+5-5S)/19=5-5(S-1)/19.

We are dealing with whole numbers of each animal so S-1 must be divisible by 19.

If S-1=19, S=20⇒C=0, number of goats=80. Note that S cannot exceed 20, because that would make C<0.

Check cost: Cows=$0, Sheep=$60, Goats=$40, total=$100. Check quantity: Cows=0, Sheep=20, Goats=80, total=100.