Fowls To Market


The farmers were bringing their fowl to market to sell for 
Christmas dinner, all nicely frozen, of course. Farmer Jones had 
three plump, nice fowl and had managed to simplify her pricing by
getting them all to the identical weight. 

Farmer Smith had geese, four of them, and he, too, had all of them
at the same weight, which was different from that of Farmer Jones's
birds. 

Three fowl from Farmer Jones and four fowl from Farmer Smith 
weighed 38 pounds. On the other hand, if Farmer Jones had had four
fowl and Farmer Smith had had three, the combined weight would 
have been 39 pounds. 

Ignoring fractional amounts, how much did each of the farmers' fowl weigh? 
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Answer:
Jones - 6 pounds each
Smith - 5 pounds each

Solution:
Let's let J stand for each of Farmer Jones' fowl, and S for Farmer Smith's.

Since Jones has 3 fowl and Smith 4 which combined weigh 38 pounds, we can
express that as 3J + 4S = 38

And since if it were switched to 4 fowl for Jones and 3 for Smith the combined 
weight would be 39, we have:  4J + 3S = 39

Simplify equation #2 and we get 3S = 39 - 4J or S = 13 - 1.3J

Substitute for J in equation 1 and we get 

3J + 4(13 - 1.3J) = 38  or  3J + 52 - 5.3J = 38

Simplify again and we get 52 - 38 = 5.3J - 3J  or 14 = 2.3J  or J = 6.08


Rounding this to 6 and substituting, we get 3(6) + 4S = 38  or  4S = 38 - 18
and 4S = 20 or S = 5.