MathDB
A 16-Quart Radiator

Source:

June 13, 2009

Problem Statement

A 16 16-quart radiator is filled with water. Four quarts are removed and replaced with pure antifreeze liquid. Then four quarts of the mixture are removed and replaced with pure antifreeze. This is done a third and a fourth time. The fractional part of the final mixture that is water is: <spanclass=latexbold>(A)</span> 14<spanclass=latexbold>(B)</span> 81256<spanclass=latexbold>(C)</span> 2764<spanclass=latexbold>(D)</span> 3764<spanclass=latexbold>(E)</span> 175256 <span class='latex-bold'>(A)</span>\ \frac{1}{4}\qquad <span class='latex-bold'>(B)</span>\ \frac{81}{256}\qquad <span class='latex-bold'>(C)</span>\ \frac{27}{64}\qquad <span class='latex-bold'>(D)</span>\ \frac{37}{64}\qquad <span class='latex-bold'>(E)</span>\ \frac{175}{256}