A fruit punch is to be made by mixing a grape wine that is 12% alcohol, a cherry

Question

A fruit punch is to be made by mixing a grape wine that is 12% alcohol, a cherry wine that is 19% alcohol, and an apricot brandy that is 42% alcohol. All percentages are based on mass. The initial mixture has twice as much apricot brandy as grape wine, and there is 50% more cherry wine than grape wine. Your host has added to the mixture 18 kg of water and 65 kg of pure grain alcohol. This produces a quantity of punch that is 33% alcohol. How much grape wine, cherry wine, and apricot brandy were mixed together before adding the water and the alcohol?

Explanation / Answer

The initial mixture has twice as much apricot brandy as grape wine.

and there is 50% more cherry wine than grape wine.

i,e if grape wine.is x then,

  apricot brandy is 2x

and  50% more cherry wine than grape wine. so cherry wine x+x/2

now x+2x+x+x/2=65kg

4.5x=65

x=65/4.5=14.44444

grape wine is x=14.44444 and

cherry wine is : x+x/5=21.666666

and apricot brandy:2x=28.888888

were mixed together before adding the water and the alcohol?

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