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This problem trains for: SAT-I, GMAT, Math Kangaroo 7-8.

What ratio of 48% alcoholic ginnix to 5% alcoholic tonnix must one mix to obtain 38% ginantonic?

(fictional drink imagined by Douglas Adams in "The Hitchhiker's Guide to the Galaxy")

Assume we have a quantity of g of ginnix and t tonnix. The ratio we are looking for is g:t in the lowest terms.The quantity of mixture obtained is g+t due to the law of conservation of mass.

equation

Divide this whole equation by t:

equation

The fraction g/t is the quantity required. Therefore, let's denote it by x and solve for it:

equation

equation

equation

equation

The ratio is 33:10.