Question 486098
A farmer has cows and chickens. He only sees 50 legs and 18 heads. How many are cows and howmany are chickens



Let the amount of cows be W, and the amount of chickens C
Then head count = W + C = 18
Leg-count = 4W + 2C = 50

We therefore have the following simultaneous equations: 


W + C = 18 -------- eq (i)
4W + 2C = 50 ------- eq (ii)
-2W - 2C = - 36 -------- eq (iii) ---- Multiplying eq (i) by - 2
2W = 14 ------- Adding eqs (ii) & (iii)


{{{W = 14/2 = 7}}}


Substituting 7 for W in eq (i), we have: 7 + C = 18


{{{C = 18 - 7 = 11}}}


There are {{{highlight_green(7)}}} cows, and {{{highlight_green(11)}}} chickens.


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Check
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Head count: cows + chickens = 7 + 11 = 18


Leg count: 7 cows + 11 chickens = 28 (7 * 4) + 22 (11 * 2) = 50