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# A mixture of nuts is to contain 3 parts cashews to 6 parts a

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A mixture of nuts is to contain 3 parts cashews to 6 parts a [#permalink]  23 Apr 2007, 05:56
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A mixture of nuts is to contain 3 parts cashews to 6 parts almonds to 7 parts walnuts by weight. How many pounds of almonds will be needed to make 5 pounds of the mixture?

(A) $$\frac{3}{8}$$

(B) $$\frac{8}{15}$$

(C) $$1\frac{1}{5}$$

(D) $$1\frac{2}{3}$$

(E) $$1 \frac{7}{8}$$
[Reveal] Spoiler: OA
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a mixture of nuts is to contain 3 parts cashews to 6 parts almonds to 7 parts walnuts by weight. How many pounds of almonds will be needed to make 5 pounds of the mixture?

a.) 3/8
b.) 8/15
c.) 6/5
d.) 5/3
e.) 15/8

First of all, write the ratios in a mixture.
The cashews, almonds and walnuts are in ratio 3:6:7
It means that, in 16 pounds of mixture, cashews are 3 pounds, almonds are 6 pounds, walnuts are 7 pounds

So in 5 pounds of mixture the almonds will be = 6*5/16 = 15/8
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c:a:w = 3:6:7

Total number of parts = 16

So 5 pounds = 16 parts.
Therefore 6 parts = 6/16 * 5 = 15/8 pounds,
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Ratio of almonds to the mixture = 6 / 16

for a mixture of 5 --> almonds = 5 x 6/16 = 30/16 = 15/8

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I write the following on my paper:

C A W = T
3 6 7 = 16
X = 5

Then after simplification X = 15/8. Answer e.
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1
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First write out the ratio:

3:6:7

Now we add x as the number of pounds of each part:

3x+6x+7x=5(the total # of pounds needed)

16x=5 --> x=5/16

This means that each pounds is 5/16 of the total.

Multiply this by the 6 parts of almonds and you get:

(5/16)*6 = 30/16 = reduces to 15/8

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Re: ratio question [#permalink]  14 Aug 2009, 00:38
what is the quickest way of solving this problem?

a mixture of nuts is to contain 3 parts cashews to 6 parts almonds to 7 parts walnuts by weight. How many pounds of almonds will be needed to make 5 pounds of the mixture?

a.) 3/8
b.) 8/15
c.) 6/5
d.) 5/3
e.) 15/8

16 x = 5 pounds , x = 5/16

Almonds weight = 5/16*6 = 15/8

also, are there any other tricks/pointers that ya'll might know of that involve ratios? thanks a lot![/quote]
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Re: ratio question [#permalink]  25 Jan 2010, 22:05
CAW
3:6:7

A = 6/16

6/16=x/5
x=15/8
Manager
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Re: ratio question [#permalink]  12 Feb 2010, 18:06
6 out of 16 => ? out of 5

solving 15/8
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Re: ratio question [#permalink]  04 Oct 2010, 16:33
16 ---------- 6

5 ----------- x

Cross multiplication:

X = 15/8

Maybe this is the easyest way to solve.
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Re: A mixture of nuts is to contain 3 parts... [#permalink]  11 Oct 2010, 13:38
1
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niheil wrote:

A mixture of nuts is to contain 3 parts cashews to 6 parts almonds to 7 parts walnuts by weight. How many pounds of almonds will be needed to make 5 pounds of the mixture?

(A) $$\frac{3}{8}$$

(B) $$\frac{8}{15}$$

(C) $$1\frac{1}{5}$$

(D) $$1\frac{2}{3}$$

(E) $$1 \frac{7}{8}$$

I feel like there's a critical piece of information that I haven't considered...

c:a:w = 3:6:7

let c= 3x; a=6x; w=7x

total weight = 16x....when 16x=5 => $$x=\frac{5}{16}$$

in this total weight contribution of almond = $$6x = 6* \frac{5}{16}$$

= $$\frac{15}{8}$$ = $$1 \frac{7}{8}$$

Hence E
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Re: A mixture of nuts is to contain 3 parts... [#permalink]  11 Oct 2010, 20:48
1
KUDOS
c:a:w=3:6:7

a=6/16*5=15/8
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Re: A mixture of nuts is to contain 3 parts... [#permalink]  11 Oct 2010, 22:47
Thanks for the help gurpreetsingh and mrinal2100.

Okay, so I see how the question was meant to be interpreted. But does anyone else think this question is a bit unclear and unfair? I know that the first sentence reads "... by weight", but it doesn't mention that the weight is 1 pound. Also, about the part of the question that reads "3 parts cashews to 6 parts almonds to 7 parts walnuts", I think this could have been more clearly stated. The sentence doesn't make it clear that 3 parts cashews weigh the same as 6 parts almonds and 7 parts walnuts.

What do you think?
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Re: A mixture of nuts is to contain 3 parts... [#permalink]  11 Oct 2010, 23:21
Niheil, the question is stated in same way as most ratio & proportion questions. There is no ambiguity. Let me try and explain this.

For the moment consider a mixture of 2 substances in the ratio 5:9 by weight. If lets say the weights of each are x and y, what we know is that :

$$\frac{x}{y}=\frac{5}{9}$$

What this means is that x & y are of the form 5A and 9A respectively for some A. Different values of A represent different choices for the pair (x,y). This is just a technique to reduce the problem from 2 variables to 1 variable to make it easier to solve.

Same technique works in 3 variable problems, so lets say x:y:z=4:7:11

$$\frac{x}{y}=\frac{4}{7}$$

So x=4A, y=7A

$$\frac{y}{z}=\frac{7}{11}$$

Since y=7A, z=11A

For each choice of A, we get a set of (x,y,z) values in the appropriate ratio.
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Re: A mixture of nuts is to contain 3 parts... [#permalink]  12 Oct 2010, 20:46
Hi shrouded1. Thanks for the explanation. It was very helpful.
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Re: ratio question [#permalink]  13 Mar 2011, 01:30
easier problem than the ones ive seen on here...
3x+6x+7x = 5
x= 5/16
6x = 6(5/16) = 5/8
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Re: ratio question [#permalink]  14 Dec 2011, 11:34
The ratios = 3:6:7
Almond in 1 pound 1*6/16 = 6/16
Almond in 5 pound = [6/16]*5= 15/8
Ans. E
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Re: ratio question [#permalink]  01 Feb 2014, 10:05
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Re: ratio question   [#permalink] 01 Feb 2014, 10:05
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