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Four brothers Adam, Bill, Charles and David together

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Four brothers Adam, Bill, Charles and David together  [#permalink]

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New post Updated on: 02 Dec 2012, 04:27
2
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

73% (03:29) correct 27% (03:48) wrong based on 116 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

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Originally posted by hardnstrong on 01 Apr 2010, 04:37.
Last edited by Bunuel on 02 Dec 2012, 04:27, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Hard Ratio question  [#permalink]

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New post Updated on: 01 Apr 2010, 06:04
34
1
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$.

Originally posted by sh00nya on 01 Apr 2010, 05:40.
Last edited by sh00nya on 01 Apr 2010, 06:04, edited 1 time in total.
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Re: Hard Ratio question  [#permalink]

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New post 01 Apr 2010, 05:02
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 :lol: ). 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 :wink:
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Re: Hard Ratio question  [#permalink]

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New post 01 Apr 2010, 06:43
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?
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Re: Hard Ratio question  [#permalink]

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New post 06 Apr 2010, 10:47
1
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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Re: Hard Ratio question  [#permalink]

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New post 08 Apr 2010, 14:18
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
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Re: Hard Ratio question  [#permalink]

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New post 01 May 2010, 01:50
4
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
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Re: Hard Ratio question  [#permalink]

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New post 02 Dec 2012, 01:01
3
(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
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Re: Four brothers Adam, Bill, Charles and David together  [#permalink]

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New post 02 Dec 2012, 04:30
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
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Re: Hard Ratio question  [#permalink]

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New post 04 Mar 2014, 22:13
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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Re: Four brothers Adam, Bill, Charles and David together  [#permalink]

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New post 26 Jan 2018, 10:48
1
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

Answer: D
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Re: Four brothers Adam, Bill, Charles and David together  [#permalink]

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Re: Four brothers Adam, Bill, Charles and David together   [#permalink] 08 Apr 2019, 11:04
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