I keep going wrong on a puzzle and I am not sure why. The puzzle is by H.E. Dudeney. Obviously I am missing something but I don't know what it is.
I've found the answer online, but having trouble with the process.
Here is the puzzle:
AT A CATTLE MARKET.
Three countrymen met at a cattle market. "Look here," said Hodge to
Jakes, "I'll give you six of my pigs for one of your horses, and then
you'll have twice as many animals here as I've got." "If that's your
way of doing business," said Durrant to Hodge, "I'll give you fourteen
of my sheep for a horse, and then you'll have three times as many
animals as I." "Well, I'll go better than that," said Jakes to Durrant;
"I'll give you four cows for a horse, and then you'll have six times as
many animals as I've got here."
No doubt this was a very primitive way of bartering animals, but it is
an interesting little puzzle to discover just how many animals Jakes,
Hodge, and Durrant must have taken to the cattle market.
Now, I get at least this far:
2H-15=J
3D-52=H
6J-21=D
But here is where I keep stumbling.
I basically am substituting on a per variable basis. Take the last equation:
6J-21=D
Substituting with the first equation I get:
6(2H-15)-21=D
12H-90-21=D
12H-69=D
Then substituting the second equation for H I get:
12(3D-52)-90-21=D
36D-624-90-21=D
36D-513=D
But I've already messed up. Where am I going wrong?
