Distributing coins trouble
There are four persons and has some coins.
gave half of the coins to
and another 4 more coins.
gave half of the coins to
and another 4 more coins.
gave half of the coins to
and another 4 more coins.
Both
and
end up with same number of coins.
How many coins did have originally?
The answer is 72.
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1 solution
Let the coins A originally had be N . Then, we have:
N ⇒ ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ A : 2 N − 4 B : 2 N + 4 ⇒ ⎩ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎧ B : 4 N − 2 C : 4 N + 6 ⇒ ⎩ ⎪ ⎨ ⎪ ⎧ C : 8 N − 1 D : 8 N + 7
B got 4 N − 2 and D got 8 N + 7
⇒ 4 N − 2 8 N ⇒ N = 8 N + 7 = 9 = 7 2