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A certain sum of money is divided among A, B and C such that A gets on [#permalink]

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17 Oct 2011, 21:13

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62% (02:14) correct
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A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $12.4 more than that received by B, find the total amount shared by A, B and C.

A. $345.20 B. $386.40 C. $520.30 D. $446.40 E. None

Re: A certain sum of money is divided among A, B and C such that A gets on [#permalink]

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17 Oct 2011, 22:29

stoy4o wrote:

A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $12.4 more than that received by B, find the total amount shared by A, B and C.

A. $345.20 B. $386.40 C. $520.30 D. $446.40 E. None

Can someone give me a short-cut on how to get to an answer?

A certain sum of money is divided among A, B and C such that A gets on [#permalink]

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01 Jul 2017, 15:16

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D The problem is not hard at all, if you get the logic of it If A has \(\frac{1}{3}\) of B and C, this means that B and C together have \(\frac{3}{3}\) . So A has 1 peace, B and C have 3 peaces, overall A has \(\frac{1}{4}\) of the total share. If we apply similar logic to B, B has\(\frac{2}{9}\). Now we can make an equality.

\(\frac{1}{4}\)x - \(\frac{1}{9}\)x = 12.4

\(\frac{(9-8)}{36}\)x = 12.4

\(\frac{1}{36}\)x = 12.4

x= 12.4*36=446.4

Hope that helped
_________________

If you find my solution useful, hit the "Kudos" button

A certain sum of money is divided among A, B and C such that A gets on [#permalink]

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01 Jul 2017, 20:02

D Just need to get an equation.

A = \(\frac{(B+C)}{3}\) = \(\frac{(total - A)}{3}\) B = \(\frac{2(A+C)}{7}\) = \(\frac{2(total - B)}{7}\)

A - B = 12.4 \(\frac{(total - A)}{3}\) - \(\frac{2(total - B)}{7}\) = 12.4 \(\frac{(7Total - 7A - 6Total + 6B)}{21}\) = 12.4 (Total - 7A + 6B)= 21*12.4 A + B + C - 7A + 6B = 21*12.4 B + C - 6A + 6B = 21*12.4 B + C - 6(A-B) = 21*12.4 B + C = 21*12.4 + 6*12.4 B + C = 27*12.4 => A = 9*12.4 A + B + C = 36*12.4 = 446.4

A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $12.4 more than that received by B, find the total amount shared by A, B and C.

A. $345.20 B. $386.40 C. $520.30 D. $446.40 E. None

Hi,

Since the method with equation is given, I will touch on an alternate method.

A bit of quick thinking at times can save you a lot of time B gets 2/7 of (B+C), so total= A+B+C=2/7*(B+C)+B+C=9/7*(B+C).. Here B+C=TOTAL*7/9.. So answer should be div by 9, only D is left.

If there are two three choices fitting in, one more calculation can get you to answer. Best if you are clueless on making equations and the choices does not have None in choices
_________________

Re: A certain sum of money is divided among A, B and C such that A gets on [#permalink]

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28 Sep 2017, 08:18

Vardan95 wrote:

D The problem is not hard at all, if you get the logic of it If A has \(\frac{1}{3}\) of B and C, this means that B and C together have \(\frac{3}{3}\) . So A has 1 peace, B and C have 3 peaces, overall A has \(\frac{1}{4}\) of the total share. If we apply similar logic to B, B has\(\frac{2}{9}\). Now we can make an equality.

Re: A certain sum of money is divided among A, B and C such that A gets on [#permalink]

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01 Oct 2017, 23:37

Vardan95 wrote:

D The problem is not hard at all, if you get the logic of it If A has \(\frac{1}{3}\) of B and C, this means that B and C together have \(\frac{3}{3}\) . So A has 1 peace, B and C have 3 peaces, overall A has \(\frac{1}{4}\) of the total share. If we apply similar logic to B, B has\(\frac{2}{9}\). Now we can make an equality.