Constant Quantity?

by YC Mak
(Singapore)

Francis, Gif and Hakim shared a sum of money. Hakim decided to give Francis 2/3 of his money. Then Francis gave Gif 3/4 of his money and Gif gave 3/7 of his money to Hakim. In the end, the amount of money they had was in the ratio of 3:6:8. If Hakim had $55 more than Francis at first, how much money did Gif have in the end?



Here's My Answer
by Zach
(Singapore)





Step 1: This question involves the Constant Total Concept as well as the Working Backwards Strategy. It is an internal transfer among 3 parties resulting in no increase in the overall total of the three people. To work backwards, we start by drawing the end ratio among the three people which is 3:6:8.

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Aug 10, 2011
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Thanks for pointing out the error!
by: Zach

Hi Phan Le,

You're right! I made a mistake there. Your solution should be the right one. I have amended the page. Thank you very much for taking time to alert me of the mistake. Greatly appreciate your kind help. Do let me know if you spot anything else "fishy". Thanks in advance. :)

Aug 10, 2011
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About a problem on the web.
by: Phan Le

In this problem: Francis, Gif and Hakim shared a sum of money. Hakim decided to give Francis 2/3 of his money. Then Francis gave Gif 3/4 of his money and Gif gave 3/7 of his money to Hakim. In the end, the amount of money they had was in the ratio of 3:6:8. If Hakim had $55 more than Francis at first, how much money did Gif have in the end?
At the end of your solution your write:

"11 units ----------> $55
1 unit ----------> $55/ 5= $11
12 units ----------> 12 x $11 = $132
Therefore, Gif had $132 in the end."
I don't understand:
I think :
11 units ----------> $55
1 unit ----------> $55/11= $5
Therefore, Gif had 12 x 5 =$60. (?)
I hope you will explain it for me.
Your sincerely.

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