Final answer:
The percentage of active property listings that are condominiums is calculated based on the proportion of new listings and the average time listings stay active. By taking into account the different average listing durations for houses and condominiums, we find that approximately 55% of the active listings are condos.
Step-by-step explanation:
To calculate the percentage of active property listings that are condominiums, we need to consider both the initial listing proportions and the average time the properties stay listed. Since 60% of new properties are houses and they stay listed for 4.5 weeks, and 40% are condominiums staying listed for 8.25 weeks, we can analyze the total listing time for each type of property over a common time frame.
Let's choose a common time frame of 8.25 weeks (the listing duration for a condominium). During this time, houses are posted and removed 1.83 times (8.25 weeks / 4.5 weeks per listing), so the effective percentage of houses listed is 60% / 1.83. For condominiums, since they stay listed for the entire 8.25 weeks, their effective percentage remains 40%.
Calculating these values:
Houses: (60% / 1.83) = 32.79%
Condominiums: remain at 40%
Now, to find the total active listings, we add both effective percentages:
Total active listings = 32.79% + 40% = 72.79%
To find the percent of active listings that are condominiums, we divide the condominium percentage by the total active listings percentage:
Percentage of condominiums = (40% / 72.79%) * 100 = 54.9%, which we can round to 55%.
Therefore, the correct answer is c. 55.