QotD: What, no horses?

I am a farmer who raise ducks and cows. The animals have a total of 9 heads and 26 feet. How many ducks and cows do I have?
Submitted by The BlueTie.

Simple,

Assume each duck and each cow has exactly one head.

Let

D = Number of Duck legs
C = Number of Cow legs

Therefore

D + C = 26

Assume also each duck has exactly two legs and each cow has exactly four legs.

Therefore

D/2 + C/4 = 9

Now we have 2 independent linear equations with 2 unknowns so it is solvable.

Take D + C = 26 and solve for D yields:

D = 26 – C

Substituting into D/2 + C/4 = 9 yields:

(26 -  C)/2  +  C/4 =  9
2(26 – C)/4 + C/4 = 9
(52 – 2C)/4 + C/4 = 9
(52 – 2C + C)/4 = 9
(52 – C)/4 = 9
52 – C = 4*9
52 – C = 36
-C =  36 – 52
-C = -16
C = 16

Thus we have 16 cow legs so either we are really sick weirdos or  we have 4 cows (16/4  = 4  since each cow has 4 legs).

Since now we know C = 16 lets substitute it into D + C = 26

D + C = 26
D + 16 = 26
D = 26 – 16
D = 10

So we have 10 duck legs.  Thus we have 5 ducks or we work for the Beijing  KFC.

Hence we have 4 cows and 5 ducks.  Simple wasn't it.

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5 Responses to QotD: What, no horses?

1. mariser says:

2. Morgat says:

ouch. mah haid hurts. I'm impressed, but mah haid hurts.

3. Brown Suga' says:

Yay, quadratic equations! I still know my math!

4. Lurkertype says:

extra points for showing all your work, tho once you know you have 4 cows, then the 5 ducks is obvious without solving the last part algebraically.

5. Lord Kalvan says:

True it was ovious but I wanted to show the step since I defined D and C as the number of duck legs and cow legs. I had not defined a variable for the number of ducks and cows. I wanted to but I wanted to use subscripts but did not know how to do that in Vox