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

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Question 486098: A farmer has cows and chickens. He only sees 50 legs and 18 heads. How many are cows and howmany are chickens
Answer by MathTherapy(10552) About Me  (Show Source):
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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%2F2+=+7

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

C+=+18+-+7+=+11

There are highlight_green%287%29 cows, and highlight_green%2811%29 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