0

This has got us stuffed but I feel there has to be a simple explanation. Q: concentrate:water are 2L:1L, 3L:2L, 1.25L:750mL, 2L:1.5L, 1.5L:800mL. If you mix all together what is the ratio? Leaving quantities as they are you get a different ratio to converting each to x:1 first. Shouldn't they be identical for both methods? Why is there a difference? I have a math degree and I feel like an idiot!

Paul Smith
  • 1
  • Welcome to MSE. Please read this text about how to ask a good question. – José Carlos Santos Sep 03 '18 at 07:14
  • I didn't quite understand what you mean by the two "methods" - in fact, I don't see even one method outlined in the question. "Leaving (...) as they are" vs "converting" - and then doing what? Surely, you cannot just blindly add up the ratios ... – Matti P. Sep 03 '18 at 10:45
  • You could just pour everything into a container and get a ratio or you could convert each ratio into an amount per litre of water then combine for 5 litres. The issue is 2+3+1.25+2+1.5:1+2+0.75+1.5+0.8 is not the same as 2+3/2+1.25/0.75+2/1.5+1.5/0.8:1+1+1+1+1 but why aren't they? – Paul Smith Sep 03 '18 at 11:53

1 Answers1

0

I would approach it like this. Consider that you're mixing substance A and substance B in different ratios in different bottles. In bottle number $i$ you have amount $A_i$ of substance A and amount $B_i$ of substance B. Then, when you add them up together, surely the amount of substance A in the final product is the sum over $i$ of $A_i$, right? $$ \sum_i A_i $$ And the amount of substance B is then $\sum_i B_i$. Therefore, the final ratio A/B of the final product is $$ \frac{ \sum_i A_i }{\sum_i A_i + \sum_i B_i} $$ I think from this on you should already know what to do.

Matti P.
  • 6,012
  • This doesn't address the difference in values of the two methods. Also, how can you have A in the formula twice and B once? The issue is 2+3+1.25+2+1.5:1+2+0.75+1.5+0.8 is not the same as 2+3/2+1.25/0.75+2/1.5+1.5/0.8:1+1+1+1+1 but why aren't they? – Paul Smith Sep 03 '18 at 10:37