Three Legged
On a farm there are three-legged-cows and chickens(reg. There are total of 83 heads and 226 legs. How many thr?
On a farm there are three-legged-cows and chickens. There are total of 83 heads and 226 legs. How many three-legged-cows are on the farm?
How would you go about solving this?
23 Chickens and 60 Three Legged Cows
Solve a set of simultaneous equations.
Let C = The number of Chickens and T = The number of three legged cows
Equation 1
C + T = 83 (equation based on the number of heads)
Therefore C = 83 – T
Equation 2.
3T +2C = 226 (equation based on the number of legs of each animal, three legged cows = 3 and chickens have 2 legs)
But from equation 1 we know that C = 83 -T, therefore substitute this into Equation 2 which now becomes:
3T + 2(83 -T) = 226
Expand the bracket
3T +166 – 2T = 226
Simplify
T +166 = 226
T = 60
As C + T = 83 it means that C = 23
Check 23 chickens x 2 legs = 46 legs
60 three legged cows = 180 legs
Total legs = 46+180 = 226 = correct
Total heads = 60+23 = 83 = correct
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