# Percentage of a percentage compared with another percentage

• May 8th 2010, 11:20 PM
ugkwan
Percentage of a percentage compared with another percentage
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.
• May 9th 2010, 06:32 PM
Anonymous1
Quote:

Originally Posted by 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.

$\displaystyle p=$ 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.