In 2000 a company increased its workforce by 50%. In 2001 it decreased its workforce by 50%. How doe

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In 2000 a company increased its workforce by 50%. In 2001 it decreased its workforce by 50%. How does the size of its workforce at the end of 2001 compare with the size of the workforce at the beginning of 2000?

Let w be the size of the workforce before any changes. We have:

• w(2000) = w(1999) * 1.5 (50% increase is the same as multiplying by 1.5)
• w(2001) = w(2000)/1.5 (50% decrease is the same as dividing by 1.5)

Substitute the first equation back into the second equation
w(2001) = w(1999) * 1.5/1.5

Cancel the 1.5 on top and bottom
w(2001) = w(1999)
This means the workforce had zero net change from the beginning of 2000 to the end of 2001.