So I’ve always considered myself fairly competent at maths and this has absolutely stumped me.
Initially my brain says obviously 40% alcohol is 2.5% stronger than 37.5% alcohol, but 2.5 is 6.666’% of 37.5, so is 40% alcohol actually 6.666’% stronger than 37.5% alcohol?
Someone help me I feel like I’m going mad
In: Mathematics
Thanks everyone, I understand now – appreciate your comments
Say you have Bottle A which is 37.5% alcohol and Bottle B which is 40% and both are 10L. Bottle B has 2.5% **more** alcohol in it than Bottle A.
>Bottle B: 10(.4) = 4L | Bottle A: 10(.375) = 3.75L
However, does this mean Bottle B is also 2.5 *times stronger* than Bottle A? Mathematically, that equation is:
>Bottle B = Bottle A * 2.5
>4L = 3.75L * 2.5
Clearly not.
>Bottle B = Bottle A * x
>Bottle B / Bottle A = x
> 4/3.75 = 1.0666
We know 1.0666 is the same as (1 + .0666), so
>Bottle B = Bottle A * (1 + .0666)
>Bottle B = Bottle A + (Bottle A)(.0666)
So how much *stronger* is Bottle B than Bottle A? We know to get from Bottle A to Bottle B we need one whole Bottle A plus another 6.666% (.0666) of Bottle A. So you can say Bottle B is 6.666 **percent** stronger or 1.0666 **times** stronger. Does that help?
You can phrase it as an addition problem, or as a multiplication problem:
* 40% is 2.5 percentage points higher than 37.5% (.375 **plus**.025 = 0.4).
* 40% is 6.67% higher than 37.5% (.375 **times** 1.0667 = 0.4).
It’s correct both ways.
I think this depends on what how you are viewing it.
If you view it as an increase 37.5/100 to 40/100 then you would increase by 2.5%
If you are viewing it as a direct percentage comparison, 40/37.5 then you are increasing the 37.5% by 6.666%
It’s 6.666% stronger because it’s in reference to the 37.5%. You could say a 40% alcohol is 2.5 percentage points higher in alcohol than a 37.5% because that is in reference to the whole volume
Edit: corrected due to my friend’s comment
You are doing percentages of percentages which is where you are having problems. 1 litre of 37.5% alcohol has 15 units of 2.5% alcohol whereas a litre of 40% alcohol has 16 units of 2.5% alcohol. So you need the difference between 15 and 16 for a percentage difference.
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