Mixing water and wine - Math Central

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Question from manish, a parent:

a man mixes three part of water to one part of wine. When he consumes
one part of mixture he realise that the drink is too dilute and hence adds one part of
wine to the remaining quantity what is the ratio of water to wine in the new mixture.

Hi Manish,

The initial mixture is one quarter wine and three quarters water.

mixture

Now he mixes it and drinks one part (one quarter of the mixture). Since it is well mixed one quarter of what he drank was wine and three quarters water. Now add to the remaining mixture an amount of wine equal to what he drank.

mixture

Now you can see that the mixture is divided into sixteen equal parts, seven of which are wine. What is the ratio of water to wine?

Penny

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