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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
joej = (x - als)/4 + 1
petes = (x - als - joej)/4 + 1
jimj = (x - als - joej - petes)/4 + 1

now als + petes = joej + jimj + 100
4als + 4petes = 4joej + 4jimj + 400
x + 4 + x - als - joej + 4 = x - als + 4 + x - als - joej - petes + 4 + 400
als + petes = 400
4als + 4petes = 1600
x + 4 + x - als - joej + 4 = 1600
2x + 8 - als - joej = 1600
8x + 32 - 4als - 4joej = 6400
8x + 32 - x - 4 - x + als - 4 = 6400
6x + 24 + als = 6400
24x + 96 + 4als = 25600
24x + 96 + x + 4 = 25600
25x + 100 = 25600
25x = 25500
x = 1020

so the total number of cattle was 1020 and the number of cattle for each person was

Al Smith 256
Joe Jones 192
Pete Smith 144
Jim Jones 108
Slim Jones 320

So the Smith family had 400 cattle and the Jones family got 720.

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