Farmer Factor Puzzle - Solution

The Puzzle:

Farmer Factor
I have decided to write a deeply moving piece of poetry for you.

First of all: Farmer Factor (who lives at Fraction Farm) wants to stock up on feed for his three types of animals (chickens, pigs, cows).

His goal is to spend all of the $100 and get exactly 100 bags altogether to fill up his cart.

Here is my poem:

    Farmer Factor took his tractor to the factory
    100 bags of feed is what his tractor will carry

    The chicken feed is first, at five dollars a bag
    Pigs need their pig feed with 3 dollars on each price tag

    And for the cows 50c a bag will feed them happily
    How did Farmer Factor spend his cash on all these three?

Naturally, each type of animal food is a different price. How does he spend his money? Happy feeding!

Our Solution:

Farmer Factor spends his money as follows: 5 bags of chicken feed ($25), 11 bags of pig feed ($33), and 84 bags of cattle fodder ($42). Total: 100 bags. Total price: $100.

[He could also have bought respectively 10 bags, 2 bags, and 88 bags but that didn't seem to be very fair to the pigs!]
Puzzle Author: Stephen Froggatt

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