SOLUTION: hagrid was doing business in hogsmeade, selling and purchasing goods. at first he doubled his money, then spend 12 galleons. he traveled further down the alley, again doubling his

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Question 786866: hagrid was doing business in hogsmeade, selling and purchasing goods. at first he doubled his money, then spend 12 galleons. he traveled further down the alley, again doubling his money, and then spending 12 galleons. on his way back to the castle he once again doubled his money and spent his last 12 galleons. how many galleons did hagrid have to begin with?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
THE ALGEBRA WAY:
x= number of Galleons Hagrid had to begin with.
Hagrid doubles his money, and then spends 12 Galleons, means he has 2x-12 after that.
Hagrid does that 3 times in a row and ends up with no money.
2%282%282x-12%29-12%29-12=0
2%284x-24-12%29-12=0
2%284x-36%29-12=0
8x-72-12=0
8x-84=0
8x=84
highlight%28x=23%2F2%29 or highlight%28x=10%261%2F2%29 or highlight%28x=10.5%29

THE FIFTH GRADER WAY:
You can work backwards (Just do a "Priori Incantatem" on Hagrid's pink umbrella).
As Hagrid was on his way back to the castle, before he spent his last 12 Galleons, he must have had exactly 12 Galleons.
Right before that, he had doubled his money, so he must have had 6 Galleons before that doubling.
Right before that, he had spent 12 Galleons, meaning that he had 18 Galleons before that spending.
Right before that, he had doubled his money, meaning that he had 9 Galleons before that doubling.
Right before that, he had spent the first 12 Galleons, meaning that he had 21 Galleons before that first spending.
However, before that, he had doubled his money for the first time, meaning that he started with 10.5 (10%261%2F2 Galleons.

NOTE:
There is a problem with that answer, because 1 Galleon is 17 Sickles (or 493 Knuts). You would have to split a coin in half, so you cannot have half a Galleon in wizarding coins. Maybe wizards use black beetle eyes for change smaller than a Knut (after all, you can get a scoop of them for 5 Knuts).

CHECKING:
At first Hagrid doubled his money (10.5 to 21 Galleons), then spend 12 Galleons (keeping 9 Galleons). He traveled further down the alley, again doubling his money (to 18 Galleons), and then spending 12 Galleons (keeping 6 Galleons). on his way back to the castle he once again doubled his money (reaching 12 Galleons), and then spent his last 12 Galleons. (Returning to Hogwars without a single Knut).