Can You get 100 percent savings?

small_unicorn

One invention saves 30% on fuel; a second, 45% ; and a third, 25% . If you use all three inventions at once can you save 100% ? If not, how much ?

from book "The Moscow puzzles" by Boris A. Kordemsky

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Rotfl

**Posted:** Tue Nov 03, 2009 3:04 pm

$LaTeX$

No, you cannot save 100%. However you can save, $100\%-(100\%-30\%)(100\%-45\%)(100\%-25\%)=100\%-(70\%)(55\%)(75\%)=\boxed{71.125\%}$ .

**Posted:** Tue Nov 03, 2009 3:28 pm

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dwei1019 · New Member Offline Joined: 17 Oct 2009 Posts: 19

how does this work???

**Posted:** Sat Nov 21, 2009 5:41 am

henrypickle

The first invention lets you only use 70% of the fuel you usually need to use. The next allows you to use 55% of the fuel you need to use (55% of the 70%), etc. You end up using about 29%, (actually about 28.8 something). Subtracting this from 100% gives the amount you save, or about 71%.

**Posted:** Sat Nov 21, 2009 8:30 pm

AIME15USAMO

Think of it like a discount at a store. If there is a shirt for 50 dollars, and it's on sale for 80% of the original price, it's sold for 40 dollars. If they put a 20% sale on this, it is once again 80% of the 40 dollar price, or 32 dollars. As a shortcut, you can do $(80%)(80%)=(.8)(.8)=.64$ If we multiply this $.64$ by our original price, 50, we get $(.64)(50)=32$ Just as we found out before, by doing one discount after another.

Hope this helps Very Happy

**Posted:** Sat Nov 21, 2009 8:40 pm

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audilover · New Member Offline Joined: 20 Nov 2009 Posts: 3

wow. good job solving that, u helped me a lot !!!! Mr. Green

**Posted:** Sat Nov 21, 2009 10:58 pm