33. Cattle Barons
Down on the Ponderosa the Smith family and the Jones family are heirs to the ranch and all its cattle. They are trying to split the cattle between them but things are getting just a tad complicated...
Al Smith took one steer more than a quarter of the whole lot. Joe Jones took one more than a quarter of those that were left. Pete Smith claimed one more than a quarter of the remainder and Jim Jones took one more than a quarter of those left.
By now the Smith brothers had between them a hundred more cattle than the Jones boys, so Slim Jones took all the rest.
How many cattle did each family end up with?
Scroll down the page for the answer.
OK, we'll call the numbers that each had als, joej, petes, jimj and slimj respectively. If x is the total number of cattle then we have
als = x/4 + 1
now als + petes = joej + jimj + 100
so the total number of cattle was 1020 and the number of cattle for each person was
Al Smith 256
So the Smith family had 400 cattle and the Jones family got 720.
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