SOLUTION: There are 41 Goats and Cocks in a farm, one Goat and Cock do not have a leg.In total there are 136 legs. How many goats and cocks are there in separately? (please explain the metho

Algebra ->  Test  -> Lessons -> SOLUTION: There are 41 Goats and Cocks in a farm, one Goat and Cock do not have a leg.In total there are 136 legs. How many goats and cocks are there in separately? (please explain the metho      Log On


   



Question 1045133: There are 41 Goats and Cocks in a farm, one Goat and Cock do not have a leg.In total there are 136 legs. How many goats and cocks are there in separately? (please explain the method)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the number of goats
Let +b+ = the number of cocks
-----------------------------
(1) +a+%2B+b+=+41+
(2) +4a+%2B+2b+-+2+=+136+
------------------------
If you add up the number of legs that +a+ number
of goats would normally have, and you add up the
number of legs that +b+ number of cocks would
normally have, and then you subtract the +2+
legs that are missing, you have the counted number
of legs: +136+
------------------------
(2) +4a+%2B+2b+=+138+
(2) +2a+%2B+b+=+69+
-----------------------
Subtract (1) from (2)
(2) +2a+%2B+b+=+69+
(1) +-a+-+b+=+-41+
--------------------
+a+=+28+
and
(1) +a+%2B+b+=+41+
(1) +28+%2B+b+=+41+
(1) +b+=+13+
------------------
There are 28 goats and 13 cocks
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check:
(2) +4a+%2B+2b+-+2+=+136+
(2) +4%2A28+%2B+2%2A13+-+2+=+136+
(2) +112+%2B+26+-+2+=+136+
(2) +138+-+2+=+136+
(2) +138+=+138+
OK