Question

on a plot of land, 48.0% of the square footage is farmland and the remaining square footage is pasture. there are buildings on exactly 23.5% of the square footage of the farmland, and there are buildings on exactly 16.0% of the square footage of the pasture. if there are buildings on exactly p% of the square footage of the plot of land, what is the value of p?

Explanation:

Step1: Find the percentage of pasture

The total land is considered as 100%. If 48.0% is farmland, then the pasture percentage is $100\% - 48.0\% = 52.0\%$.

Step2: Calculate building percentage on farmland

The percentage of farmland with buildings is $48.0\% \times 23.5\%$. Let's calculate that: $0.48\times0.235 = 0.1128$ or 11.28%.

Step3: Calculate building percentage on pasture

The percentage of pasture with buildings is $52.0\% \times 16.0\%$. Calculating: $0.52\times0.16 = 0.0832$ or 8.32%.

Step4: Sum the two building percentages

To find the total percentage of the plot with buildings, we add the two percentages: $11.28\% + 8.32\% = 19.6\%$.

Answer:

19.6