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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?

 Sep 17, 2021
 #1
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Did Anne give 1/2 of her original money to Bernard or 1/2 of the remaining money?

 Sep 18, 2021
 #2
avatar+32645 
+2

Like so:

 

 Sep 18, 2021
 #3
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+1

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.

 Sep 19, 2021

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