Problem: A 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:
Answer Choices:
A. 1/4
B. 81/256
C. 27/64
D. 37/64
E. 175/256
Solution:
RemovalsFirstSecondThirdFourth​Water drawn43241​11611​​Water left129643​5161​​Antifreeze drawn01143​2165​​Antifreeze left43+4=7541​+4=941​61615​+4=101615​​​
165161​​=25681​
16101615​​=256175​