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# Four brothers Adam, Bill, Charles and David together

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Manager
Joined: 05 Mar 2010
Posts: 200

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01 Apr 2010, 03:37
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55% (hard)

Question Stats:

74% (03:04) correct 26% (04:23) wrong based on 145 sessions

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Four brothers Adam, Bill, Charles and David together contributed certain amount of money and purchased a car. The contribution made by Adam is half that of the total contribution made by the other three brothers, contribution made by Bill is one-fourth of the total contribution made by the other three brothers and the contribution made by Charles is two-third of the total contribution made by the other three brothers. If the total price of the car is $9900, find the contribution made by David. A.$540
B. $580 C.$600
D. $660 E.$680
[Reveal] Spoiler: OA

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Last edited by Bunuel on 02 Dec 2012, 03:27, edited 1 time in total.
Renamed the topic and edited the question.
Senior Manager
Joined: 31 Mar 2010
Posts: 412
Location: Europe

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01 Apr 2010, 04:02
Hmm, if you write it down you get literally:

$$A = \frac{1}{2}(B + C + D)$$

$$B = \frac{1}{4}(A + C + D)$$

$$C = \frac{2}{3}(A + B + D)$$

$$A + B + C + D = 9900$$

Therefore you have a system of 4 unknowns and 4 equations, so it's solvable (too bad it's not a DS problem we could just stop here ). Now I guess the easiest way to solve it is to use Gauss' Pivot Method? Remember you are only interested in D, so no need to calculate A, B and C, that would be a waste of time
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01 Apr 2010, 04:40
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Given that A:(B+C+D)= 1:2.
Hence A contributed 1/3rd of the total price.

Given B:(A+C+D)=1:4
Hence B contributed 1/5th of the total price.

Given C:(A+B+D)=2:3
Hence C contributed 2/5th of the total price.

Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15

So, the remaining 1/15th of the price is contributed by David.
Hence David's contribution= 1/15×9900=660$. Last edited by sh00nya on 01 Apr 2010, 05:04, edited 1 time in total. Senior Manager Joined: 31 Mar 2010 Posts: 412 Location: Europe Re: Hard Ratio question [#permalink] ### Show Tags 01 Apr 2010, 05:43 sh00nya wrote: Given that A:(B+C+D)= 1:2. Hence A contributed 1/3rd of the total price. Hi, I don't understand where you get the 1/3 from? Manager Joined: 19 Jul 2009 Posts: 50 Location: baltimore, md Schools: kellogg, booth, stern, ann arbor Re: Hard Ratio question [#permalink] ### Show Tags 06 Apr 2010, 09:47 1 This post received KUDOS sh00nya wrote: Given that A:(B+C+D)= 1:2. Hence A contributed 1/3rd of the total price. Given B:(A+C+D)=1:4 Hence B contributed 1/5th of the total price. Given C:(A+B+D)=2:3 Hence C contributed 2/5th of the total price. Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15 So, the remaining 1/15th of the price is contributed by David. Hence David's contribution= 1/15×9900=660$.

how did you get the contributed amounts? for example A contributed 1/3, B contributed 1/5th, etc?
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08 Apr 2010, 13:18
azule45 wrote:
sh00nya wrote:
Given that A:(B+C+D)= 1:2.
Hence A contributed 1/3rd of the total price.

Given B:(A+C+D)=1:4
Hence B contributed 1/5th of the total price.

Given C:(A+B+D)=2:3
Hence C contributed 2/5th of the total price.

Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15

So, the remaining 1/15th of the price is contributed by David.
Hence David's contribution= 1/15×9900=660$. how did you get the contributed amounts? for example A contributed 1/3, B contributed 1/5th, etc? Add the portions of the ratio. 1:2 => 3 parts total, A is 1/3 1:4 => 5 parts total, B is 1/5 2:3 => 5 parts total, C is 2/5 Manager Joined: 29 Dec 2009 Posts: 110 Location: india Re: Hard Ratio question [#permalink] ### Show Tags 01 May 2010, 00:50 4 This post received KUDOS there is another simple way ---- a+b+c+d=t a= .5(t-a) b= .25(t-b) c=2/3(t-c) so t = 9900 so a=3300 , b= 1980 , c= 3960 so d= 660 Senior Manager Joined: 13 Aug 2012 Posts: 456 Concentration: Marketing, Finance GPA: 3.23 Re: Hard Ratio question [#permalink] ### Show Tags 02 Dec 2012, 00:01 3 This post received KUDOS (1) A = (B + C + D)/2 (2) B = (A + C + D)/4 (3) C = 2(B + D + A)/3 (4) A + B + C + D = 9900 Combine (1) and (4) A = (9900 - A)/2 ==> A=3300 Combine (2) and (4) B = (9900 - B)/4==>B=1980 Combine (3) and (4) C = 2(9900-C)/3==>C=3960 D = 9900 - (3300 + 1980 + 3960) D = 660 Answer: 660 _________________ Impossible is nothing to God. Math Expert Joined: 02 Sep 2009 Posts: 43789 Re: Four brothers Adam, Bill, Charles and David together [#permalink] ### Show Tags 02 Dec 2012, 03:30 hardnstrong wrote: Four brothers Adam, Bill, Charles and David together contributed certain amount of money and purchased a car. The contribution made by Adam is half that of the total contribution made by the other three brothers, contribution made by Bill is one-fourth of the total contribution made by the other three brothers and the contribution made by Charles is two-third of the total contribution made by the other three brothers. If the total price of the car is$9900, find the contribution made by David.

A. $540 B.$580
C. $600 D.$660
E. $680 Similar question to practice: baker-s-dozen-128782-20.html#p1057509 _________________ SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1839 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: Hard Ratio question [#permalink] ### Show Tags 04 Mar 2014, 21:13 sh00nya wrote: Given that A:(B+C+D)= 1:2. Hence A contributed 1/3rd of the total price. Given B:(A+C+D)=1:4 Hence B contributed 1/5th of the total price. Given C:(A+B+D)=2:3 Hence C contributed 2/5th of the total price. Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15 So, the remaining 1/15th of the price is contributed by David. Hence David's contribution= 1/15×9900=660$.

Nice method to solve this kind of problems, when only 1 variable value is required
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26 Jan 2018, 09:48
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Expert's post
hardnstrong wrote:
Four brothers Adam, Bill, Charles and David together contributed certain amount of money and purchased a car. The contribution made by Adam is half that of the total contribution made by the other three brothers, contribution made by Bill is one-fourth of the total contribution made by the other three brothers and the contribution made by Charles is two-third of the total contribution made by the other three brothers. If the total price of the car is $9900, find the contribution made by David. A.$540
B. $580 C.$600
D. $660 E.$680
]

We can let the contribution made by Adam, Bill, Charles and David be A, B, C, and D respectively.

Since Adam contributes A dollars, the other three boys contribute 9900 - A dollars; so we have:

A = (1/2)(9900 - A)

2A = 9900 - A

3A = 9900

A = 3,300

Similarly, since Bill contributes B dollars, the other three boys contribute 9900 - B dollars and we have:

B = 1/4(9900 - B)

4B = 9900 - B

5B = 9900

B = 1,980

Finally, since Charles contributed C dollars, the other three boys contributed 9900 - C dollars and thus:

C = 2/3(9900 - C)

3C = 2(9900) - 2C

5C = 2(9900)

C = 3,960

Now that we know A = 3,300, B = 1,980 and C = 3,960, we can easily find D by the following equation:

3,300 + 1,980 + 3,960 + D = 9,900

9,240 + D = 9,900

D = 660

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Re: Four brothers Adam, Bill, Charles and David together   [#permalink] 26 Jan 2018, 09:48
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