Adding percentages

mmac684

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Aug 5, 2014
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Here's the problem: if gas goes up 8% the first year, 15% the second year and 20% the third year what is the overall percentage increase? I know that you can't simply add 8+15+20, but I don't know the way to figure this out. Can you help? Thanks!!
 
Hello, mmac684!

If gas goes up 8% the first year, 15% the second year
and 20% the third year, what is the overall percentage increase?
I know that you can't simply add 8+15+20. . Right!
An 8% increase means the new price is 1.08x\displaystyle 1.08x

A 15% increase means the new price is 1.15(1.08x)\displaystyle 1.15(1.08x)

A 20% increase means the new price is 1.20(1.15)(1.08x)\displaystyle 1.20(1.15)(1.08x)

The final price is: 1.20(1.15)(1.08x)=1.4904x\displaystyle 1.20(1.15)(1.08x) \:=\:1.4904x

The final price is 49.04%\displaystyle 49.04\% larger than the original x.\displaystyle x.

The overall percentage increase is 49.04%.\displaystyle 49.04\%.
 
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