# Figuring out this riddle using algebra

**URL:** <https://boards.straightdope.com/t/figuring-out-this-riddle-using-algebra/280811>\
**Category:** Factual Questions\
**Created:** [December 20, 2004, 4:29pm UTC](https://boards.straightdope.com/t/figuring-out-this-riddle-using-algebra/280811 "2004-12-20T16:29:34Z")\
**Posts on this page:** 2\
**Page:** 2

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**Author:** ![vetbridge](https://avatars.discourse-cdn.com/v4/letter/v/b5e925/32.png) [@vetbridge](https://boards.straightdope.com/u/vetbridge)\
**Post date:** [December 21, 2004, 4:49pm UTC](https://boards.straightdope.com/t/figuring-out-this-riddle-using-algebra/280811/21 "2004-12-21T16:49:24Z")

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> [@vd](#):
>
> But it’s not really out of line for high-end drafting/drawing pencils at $10.77 a dozen.
> 
> [http://www.staples.com/catalog/search/Search\_Sum.asp?PageType=2&SearchPageType=2&cromulent=&Keywords=turquoise&image1.x=0&image1.y=0&IpClassId=110200&IpSessionId=217116864082&IpClassCount=7](http://www.staples.com/catalog/search/Search_Sum.asp?PageType=2&SearchPageType=2&cromulent=&Keywords=turquoise&image1.x=0&image1.y=0&IpClassId=110200&IpSessionId=217116864082&IpClassCount=7)

My mistake. I assumed that someone having trouble figuring out the cost of a couple pencils would be looking more for low-end number twos.

J/K of course;)

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**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\
**Post date:** [December 21, 2004, 5:15pm UTC](https://boards.straightdope.com/t/figuring-out-this-riddle-using-algebra/280811/22 "2004-12-21T17:15:02Z")

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This question (and questions very similar to it) are pretty common basic algebra word problems, because they’re straightforward if you take the algebraic approach, but if you try to answer them just off the top of your head, it’s easy to get the wrong answer—to jump to the conclusion that **x-ray vision** started with in Post #16? (something like that—@#!%\* Preview won’t show post numbers) but then not to notice that it wouldn’t work.

> [@Jurph](#):
>
> X + Y = 1.10  
> X - Y = 1.00
> 
> Since both equations are true, you can “add” them ( **Mathochist** will be along with a proof I’m sure 😉 )

I’m not **Mathochist** , but in case anybody’s still wondering why you can “add” two equations together:

It’s legal to add the same number to both sides of an equation, right? So I could take an equation like X + Y = 1.10 and add the same number to both sides, and it would be equivalent to the equation I started with.

Now the second equation is telling me that X - Y and 1.00 are equal—that they represent the same number. When I add the two equations together, adding X-Y to X+Y and 1.00 to 1.10, I’m just adding the same number to both sides of X + Y = 1.10. So the resulting equation is true whenever the original two were.

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