Adding percentages

[mmac684]

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!!

 

[soroban]

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 \(\displaystyle 1.08x\)

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

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

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

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

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