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!
2026-03-25 10:53:43.1774436023
Cordial Ratios - per litre compared to as is
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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.