Question

Charlie had $5 notes only and George had only $2 notes. The number of notes Charlie had was 2/3 of the number of notes George had. After George gave Charlie $80, Charlie exchanged the money to $5 notes. In the end, the number of notes George had became 10% more than the number of notes Charlie had. How much money did George have in the end.

Answer 1

at the beginning:
number of $2 notes for George --- 3x
number of $5 notes for Charlie --- 2x , (this avoids fractions)

George gave $80 to Charlie in $2 notes, or he gave Charlie 40 of his
$2 notes,
so now George has 3x-40 of the $2 notes
Charlie wants the $80 in $5 notes, which would be 16 of them,
so now Charlie has 2x + 16 of the $5 notes

"the number of notes George had became 10% more than the number of notes Charlie had"
---> 3x-40 = 1.1(2x+16)
times 10 to get rid of decimals
30x - 400 = 11(2x + 16)
30x - 400 = 22x + 176
8x = 576
x = 72

since now George has 3x-40 of the $2 notes,
he has 3(72) - 40 or 176 of the $2 notes, which means he has $352.

let's check this out:
at the start
George has 3x or 216 of the $2 notes, so he has $432
Charlie has 2x or 144 of the $5 notes, so he has $720

after the exchange:
George has 432-80 = $352, in twos that would be 176 notes
Charlie has 720+80 = $800, in fives that would be 160
What is 10% more than 160 ? .... 160+16 = 176
Yeahhh!!!!