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# Help me to solve this problem

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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
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Like so:

Sep 18, 2021
#3
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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