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

Ratio of almonds to the mixture = 6 / 16

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

Answer: E

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

Answer: E

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

c:a:w=3:6:7

a=6/16*5=15/8
e is the answer

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.

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]

CAW
3:6:7

A = 6/16

6/16=x/5
x=15/8

6 out of 16 => ? out of 5

solving 15/8

16 ---------- 6

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

Cross multiplication:

X = 15/8

Maybe this is the easyest way to solve.

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?

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.

Hi shrouded1. Thanks for the explanation. It was very helpful.

easier problem than the ones ive seen on here...
3x+6x+7x = 5
x= 5/16
6x = 6(5/16) = 5/8

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

This question is a great candidate for approximation.

The total ratio 16x can be approximated to 15x, which can then be divided by 3 to get 5x.

Dividing almond's ratio of 6x by 3 equals 2x. However, it will be a tiny bit less than 2x because we rounded down the total ratio.

Answer choice E fits the bill.