# Percentage of a percentage compared with another percentage

#### ugkwan

Im having a tough time evaluating this word problem.
If 47 percent of the population are working class, and the other 53 percent of the population are upper class. Then if 37 percent of the whole upperclass, which is 53 percent of the total population are the owners of the factories where the working class work, what is the percentage population of the factory owners in terms of the total population.

#### Anonymous1

Im having a tough time evaluating this word problem.
If 47 percent of the population are working class, and the other 53 percent of the population are upper class. Then if 37 percent of the whole upperclass, which is 53 percent of the total population are the owners of the factories where the working class work, what is the percentage population of the factory owners in terms of the total population.
$$\displaystyle p=$$ pop; $$\displaystyle u=$$ upper; $$\displaystyle w=$$ working; $$\displaystyle f=$$ factory owner.

Convince yourself that,

$$\displaystyle .53p = u$$

Also,

$$\displaystyle .37u = f \implies .37\cdot (.53p) = f \implies .1961p = f.$$

That is, $$\displaystyle 19.61$$% of the population are factory owners.

• ugkwan and masters