Very unimportant maths question

[Orangewall]

Please settle a debate!

Three people split two excellent bottles of French white on a Thursday evening. Due to glass sizes and generous servings this amounts to one glass per bottle per person. One of the party is claiming that we’ve had two thirds of the wine each because we’ve had two bottles. I say that’s impossible because there are only three of us and that we’ve had one third of the total quantity (two bottles.)

Please. PLEASE help us settle this because at this point the only way to solve it is to drink another two bottles.

The other person is right.

You've each had two thirds of a bottle but one third of the total wine.

You each had one third of each bottle, so one third of the total quantity of wine, i.e two thirds of a bottle each. How's your head today?

You've had two thirds of a bottle each. Wine fuelled miscommunication perchance?

You are correct. 1/3 each of the total two bottles. 2/6 I think is where they are getting confused?

You can't have 2/3 each if there are 3 of you? 2/3 x 3 = 6/3?

But my maths skills are not to be trusted!

One of the party is claiming that we’ve had two thirds of the wine each because we’ve had two bottles.

If you change to say

One of the party is claiming that we’ve had two thirds of a bottle each because we’ve had two bottles.

Then it works.

And you’ve had one third of the total each as well.

You each had 1/3 of a bottle and 1/3 of the total amount. If there is 3 glasses per bottle, and you had 2 bottles that is 6 glasses. You each had 2 glasses, so 2/6 which simplifies to 1/3. You should probably drink the other two bottles to be sure though.

Well each had 2/3rd of a bottle, 1/3 each overall

No they aren’t - not as phrased

It is ambiguous as it is not clear whether you have only had one bottle or finished both!

Those are massive glasses btw!

They are a large measure in a pub.

There were 6 glasses served in total. Each person had 2 so 2/6 which is the same as 1/3.

Thanks all, it’s turning into a maths gcse paper here at the moment, we’ve had two rounds of practical demonstrations with glasses of water and still fiercely defending our corners 😂

My vote Is to have two more bottles

We’ve discussed further and my solution is that we put two bottles into a Greek style carafe and redo the experiment

Good idea, enjoy your night!

I think both could be right. You all had one third of the wine consumed or two thirds of a bottle.

You have each had 2/3 of a bottle of wine which equates to 1/3 of the total amount of wine in both bottles!
Maths teacher here!

You’ve each drunk 2/3 of a bottle of wine. You have each drunk 1/3 of the total quantity of wine.

There are 2 bottles so technically there are 6 lots of 1/3 available for consumption. If you all had an equal amount that means that you had 2/3 of a bottle each. However as it was split equally you all had 1/3 of the total amount of available wine each.

Alternatively in millilitres there were 1500ml (assuming standard bottle of 750ml). You all consumed 500ml each as it split equally. This means you all had 1/3 of the total amount which is 2/3 of a bottle.

You’ve had 2 of 6 glasses each - so 2/6 -1:3 of the total wine

You have each had 2/3 of a bottle so 500 ml. As you had 2 bottles that means you've each had 1/3 of each bottle.

perhaps next time you go out, order the bottles to avoid confusion?

Average bottle is 750ml x 2 = 1500ml ÷3 = 500ml so 2/3 of a bottle each?

You obviously need more wine 😂