Question about ratio word problem

Question

Here is the question and solutions:

It is possible that there are 10 cups of peanuts, 6 cups of walnuts, 4 cups of cashews. So total number of cups in this mix is 20. So 10:6:4 can be reduced to 5:3:2.
Another combination of the mix could be 20 cups of peanuts, 12 cups of walnuts, and 8 cups of cashews. So the total number of cups in this mix is 20+12 +8= 40 So 20:12:8 could be reduced to 5:3:2.

So I do not know how many cups of party mix based on the ratio 5:3:2 as this ratio could be reduced.

Without know how many cups of party mix, how is the answer between 3 and 4?

Thanks!

Answer 1

The question says you are making $12$ cups of party mix. All the quantities in $5:3:2$ need to be multiplied by $\frac{12}{10}$

Answer 2

Okay, consider "per cup of party mix", you need exactly $0.5$ cups of peanuts, $0.3$ cups of walnuts, $0.2$ cups of cashews -- does this make sense? Irrespective of number of total cups of mix made. I'd say we "norm" the ratios to have the sum of $1$.
So you only need to multiply $0.3$ by $12$ to get the desired result.