Antifreeze and Water

A quart bottle contains a mixture that is 1/3 antifreeze and 2/3 water. A half-gallon bottle contains a mixture that is 3/4 antifreeze and 1/4 water. The contents of the two bottles are poured into a gallon jug. In the form a:b, what is the ratio of antifreeze to water in the jug?
Source: NCTM Mathematics Teacher

SOLUTION
We convert all measure to quarts.
Amounts in the quart bottle
1/3 quart antifreeze
2/3 quart water

Amounts in the half-gallon (2 quarts) bottle
\displaystyle\frac{3}{4}\left (2\right )=\frac{3}{2} quarts antifreeze
\displaystyle\frac{1}{4}\left (2\right )=\frac{1}{2} quart water

Amounts in the gallon jug
\displaystyle\frac{1}{3}+\frac{3}{2}=\frac{11}{6} quarts antifreeze
\displaystyle\frac{2}{3}+\frac{1}{2}=\frac{7}{6} quart water

Ratio of antifreeze to water in the gallon jug
\displaystyle\frac{11}{6}:\frac{7}{6}
Simplify
11:7

Answer: 11:7

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About mvtrinh

Retired high school math teacher.
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