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The first mixture consists of its 3/4 is peanuts and the rest is cashe

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The first mixture consists of its 3/4 is peanuts and the rest is cashe [#permalink]

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New post 01 Mar 2016, 23:38
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The first mixture consists of its 3/4 is peanuts and the rest is cashews. The second mixture has the same quantity of cashews as the first mixture but the peanuts’ quantity of the second mixture is 8 pounds fewer than that of the first mixture. If the ratio of the peanuts to cashews is 7 to 3 in the second mixture, what is the amount of the peanuts quantity in the first mixture, in pounds?

A. 24
B. 28
C. 32
D. 36
E. 40


* A solution will be posted in two days.
[Reveal] Spoiler: OA

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Re: The first mixture consists of its 3/4 is peanuts and the rest is cashe [#permalink]

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New post 02 Mar 2016, 05:25
MathRevolution wrote:
The first mixture consists of its 3/4 is peanuts and the rest is cashews. The second mixture has the same quantity of cashews as the first mixture but the peanuts’ quantity of the second mixture is 8 pounds fewer than that of the first mixture. If the ratio of the peanuts to cashews is 7 to 3 in the second mixture, what is the amount of the peanuts quantity in the first mixture, in pounds?

A. 24
B. 28
C. 32
D. 36
E. 40


* A solution will be posted in two days.


Let the quantity of first mixture be x and that of second be y.
Cashews in both mixtures is same..
so \(\frac{1}{4}*x=\frac{3}{10}* y\)..
so \(x= \frac{6}{5} y\)...

Now lets work on peanuts..
Peanuts in first =\(\frac{3}{4} x\)=\(\frac{3}{4}* \frac{6}{5}y\)..
peanuts in second Mix=\(\frac{7}{10} y\)..
Given:-
\(\frac{3}{4} x\)=\(\frac{3}{4}* \frac{6}{5}y-\frac{7}{10} y\)=8..
y=40..
so \(x= \frac{6}{5}* 40=48\)..
\(peanuts= \frac{3}{4} * 48 =36\)..
ans D

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Re: The first mixture consists of its 3/4 is peanuts and the rest is cashe [#permalink]

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MathRevolution wrote:
The first mixture consists of its 3/4 is peanuts and the rest is cashews. The second mixture has the same quantity of cashews as the first mixture but the peanuts’ quantity of the second mixture is 8 pounds fewer than that of the first mixture. If the ratio of the peanuts to cashews is 7 to 3 in the second mixture, what is the amount of the peanuts quantity in the first mixture, in pounds?

A. 24
B. 28
C. 32
D. 36
E. 40


* A solution will be posted in two days.


Given:

Mixture 1: C:P = 3:1
Mixture 2: C:P = 7:3

Mixture 2: Mixture 1 = 7:3:9 (Ratio properties. If A:B = 2:5 and B:C = 1:2, Then A:B:C = 2:5:10. Similar one we are applying here.)
C2:P:C1

The difference of two in the ratio is due to the removal of 8 pounds. I.e 2X = 8, then 9X = 36 and 7X = 28. Hence the answer is 36.
IMO D

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The first mixture consists of its 3/4 is peanuts and the rest is cashe [#permalink]

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New post 02 Mar 2016, 16:28
let x=total weight of first mixture
weight of peanuts in second mixture=(3x/4)-8
weight of cashews in second mixture=x/4
(3x/4)-8/(x/4)=7/3
x=48 pounds
3(48)/4=36 pounds of peanuts in first mixture

Last edited by gracie on 05 Mar 2016, 13:53, edited 1 time in total.

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Re: The first mixture consists of its 3/4 is peanuts and the rest is cashe [#permalink]

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The first mixture consists of its 3/4 is peanuts and the rest is cashews. The second mixture has the same quantity of cashews as the first mixture but the peanuts’ quantity of the second mixture is 8 pounds fewer than that of the first mixture. If the ratio of the peanuts to cashews is 7 to 3 in the second mixture, what is the amount of the peanuts quantity in the first mixture, in pounds?

A. 24
B. 28
C. 32
D. 36
E. 40

This is frequently given on GMAT MATH, which is “2 by 2” question.
Attachment:
mixture.jpg
mixture.jpg [ 10.63 KiB | Viewed 1026 times ]

On the table above, 3f-8:f=7:3 -> 3(3f-8)=7f, 9f-24=7f, f=12. Hence, in the first mixture, peanuts=3f=3(12)=36 is the answer. Therefore, D is the answer.
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Re: The first mixture consists of its 3/4 is peanuts and the rest is cashe [#permalink]

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New post 18 Nov 2017, 05:33
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MathRevolution wrote:
The first mixture consists of its 3/4 is peanuts and the rest is cashews. The second mixture has the same quantity of cashews as the first mixture but the peanuts’ quantity of the second mixture is 8 pounds fewer than that of the first mixture. If the ratio of the peanuts to cashews is 7 to 3 in the second mixture, what is the amount of the peanuts quantity in the first mixture, in pounds?

A. 24
B. 28
C. 32
D. 36
E. 40


* A solution will be posted in two days.


Its an old question but I found a slightly different way to approach it than the listed methods.

In the first mixture, Peanuts are 3/4 and consequently cashews are 1/4. Their ratio:

\(\frac{c}{p} = \frac{1}{3}\)

\(c = \frac{p}{3}\)

In mixture 2:

\(\frac{c}{p-8} = \frac{3}{7}\)

\(7c = 3(p-8)\)

from the first mixture equation, we know \(c = \frac{p}{3}\)

\(7*\frac{p}{3} = 9p - 72\)

simplifying

\(72 = 9p - 7p\)

\(2p = 72\)

\(p = 36\)
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Re: The first mixture consists of its 3/4 is peanuts and the rest is cashe   [#permalink] 18 Nov 2017, 05:33
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