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

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23 Apr 2007, 06:56

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26% (01:31) wrong based on 218 sessions

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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 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

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]

Re: A mixture of nuts is to contain 3 parts... [#permalink]

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11 Oct 2010, 14:38

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niheil wrote:

Please help with this question:

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 = \(6x = 6* \frac{5}{16}\)

Re: A mixture of nuts is to contain 3 parts... [#permalink]

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11 Oct 2010, 23:47

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.

Re: A mixture of nuts is to contain 3 parts... [#permalink]

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12 Oct 2010, 00:21

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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