David had 75 filters to post around town. Last week, he posted 2/5 of them. This week he posted 2/3 of the remaining filters. How many filters has he not posted?

Answer: 15 filters are not posted by David. Solution: Given that David had 75 filters to post around town. Last week David posted [tex]\frac{2}{5}[/tex] of them. This week he posted [tex]\frac{2}{3}[/tex] of remaining filters. Need to determine number of filters not posted by David. Let’s first calculate exact number of posters posted by David in two weeks. Number of filter posted by David in last week = [tex]\frac{2}{5}[/tex] of total filters = [tex]\frac{2}{5}[/tex] of 75 [tex]= \frac{2}{5} \times 75 = 30 filters[/tex]Remanding filters in this week = 75 – 30 = 45 Now from information given for this week, number of filters posted = [tex]\frac{2}{3}[/tex] of remaining filters = [tex]\frac{2}{3}[/tex] of 45 = 30 posters. So number of filters posted in two weeks = 30 + 30 = 60 filters So filters not posted = 75 – 60 = 15 Hence 15 filters are not posted by David.