Catherine had some money at first. She gave 1/4 of her money to Anne. As a result, Anne had thrice as much as before. Then, Anne gave 1/2 of her money to Bernard. Bernard then had 1 1/2 times as much money as before. Anne still had $129 left. How much money did each child have at first?
+308 Did Anne give 1/2 of her original money to Bernard or 1/2 of the remaining money?
Let Anne, Bernard and Catherine had A, B and C
amount of money (in dollars), separately
at first
Catherine gave 1/4 of C to Anne now
Anne have A + 1/4C
Catherine have C - 1/4C = 3/4C
given Anne had thrice as much as before
=> A + 1/4C = 3A => 2A + 1/4C = 0
Now Anne gave 1/2 of (A + 1/4C) to Bernard now
Bernard have B + 1/2A + 1/8C
Anne have 1/2A + 1/8C
given Bernard had 1 1/2 times as much as before
=> B + 1/2A + 1/8C = 3/2B
=> 1/2A - 1/2B + 1/8C = D
=> 4A - 4B + C = D
also Anne still had $129 left then
=> 1/2A + 1/8C = 129
We have -2A + 1/4C = D
4A - 4B + C = D
1/2A + 1/8C = 129
-2A - A = -2 * 129
-3A = 2 * 129
A = -2 * 43
So A = 86 now 2A + 1/4C = D
=> 1/4C = 2A = 2 * 86 => C = 8 * 85
=> C = 688
4 * 86 - 4B + 688 = D
=> 4B = 688 + 4 * 85
=> B = 172 + 86 = 258
B = 258
Anne had $85, Bernard had $258 and Catherine had $688 at first.
