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

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

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02 Mar 2016, 00:38
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Question Stats:

73% (01:58) correct 27% (02:25) wrong based on 126 sessions

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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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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 5732 Re: The first mixture consists of its 3/4 is peanuts and the rest is cashe [#permalink] ### Show Tags 02 Mar 2016, 06:25 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 _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html GMAT online Tutor Manager Joined: 25 Dec 2012 Posts: 133 Re: The first mixture consists of its 3/4 is peanuts and the rest is cashe [#permalink] ### Show Tags 02 Mar 2016, 09:24 1 This post received KUDOS 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 Director Joined: 07 Dec 2014 Posts: 929 The first mixture consists of its 3/4 is peanuts and the rest is cashe [#permalink] ### Show Tags 02 Mar 2016, 17:28 1 This post received KUDOS 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, 14:53, edited 1 time in total. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5079 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The first mixture consists of its 3/4 is peanuts and the rest is cashe [#permalink] ### Show Tags 03 Mar 2016, 18:20 2 This post received KUDOS Expert's post 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 [ 10.63 KiB | Viewed 1156 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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Manager
Joined: 14 Oct 2015
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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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18 Nov 2017, 06:33
2
KUDOS
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, 06:33
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