## 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: $11:7$