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Question 296591: Anne, Bernard and Charlotte each had some pennies. They decided to divide their pennies in the following way. Bernard gave one-half of his pennies to Charlotte and kept the rest. Anne then gave one-third of her pennies Bernard and one-sixth of them to Charlotte. At the end, each had 27 pennies. How many pennies did Charlotte have originally?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Anne, Bernard and Charlotte each had some pennies. They decided to divide their pennies in the following way. Bernard gave one-half of his pennies to Charlotte and kept the rest. Anne then gave one-third of her pennies Bernard and one-sixth of them to Charlotte. At the end, each had 27 pennies. How many pennies did Charlotte have originally?
At the end they all had 27 pennies each.
So total pennies available = 27 * 3= 81
let bernard have x
and anne have y
Let charolette have z
charlotte has 1/2 x +1/6 y + z =27
bernard has 1/2 x +1/3 y=27 ( he gave half to charlotte and got 1/3 from anne)
Anne has y-(1/3 y +1/6 y) = 27 ( anne gave 1/3 to bernard and 1/6 to charolette
= y-1/2 y = 27
1/2 y =27
y=54 The pennies Anne has
Since y= 54
Bernard will have 1/2x+ 1/3 * 54 =27
=1/2 x = 9
x=18 the pennies bernard has
Charolette has the balance ie: 9
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