Young McDonald's Animals
When Old McDonald was young and had just started his farm, animals were cheaper then. Each cow costed $10, every pig $3, and every chicken $0.50 [they ate a lot of chicken].
When Young McDonald had started his farm, he spent exactly $100 and had bought 100 animals.
How many chickens did he buy when he first started his farm?
Assume he bought a non-zero number of cows, pigs, and chickens.
The answer is 94.
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1 solution
If we write the number of cows as c, the number of pigs as p, and the number of chickens as h, we know that:
10c+3p+1/2h=100 [for the dollar amounts] and
c+p+h=100 [for the amount of animals]
If you double the first equation, you get:
20c+6p+h=100
Subtract the second equation from this to get:
19c+5p=100
We see very quickly that the values of c and p have to be 5 and 1. Now subtract this value from the total number of animals.
100-[5+1]=94, the amount of chickens!
[Not one of my better problems, but it works :/]