Ugh, algebra

[telophase]

OK, I am rather NOT ashamed to admit I retain about zilch of my algebra. *insert melodramatic cries of "But I am an artist!!!" here*

ETA: solved. :)

I'm trying to work out what the real price of an item should be if that price plus sales tax makes a round number. (i.e., I really don't want to mess with change at A-Kon, and I don't want to eat the sales tax, either.)

So ... if the final round number price is $8.00 and the sales tax rate is 8.25%, what should the "real" price be? I think I can dredge up enough knowledge to set up the equation, but not enough to actually solve it correctly, because I seem to end up with the answer being the tax rate on $1.00 when I try.

It *should* be: X + X(.0825) = 8

I think.

*headache*

Help appreciated, as well an explanation of what you did, so I can repeat it for 2 more prices, plzkthnx.



Honestly, you'd never know I went all the way through calculus in highschool, with a B average. Well, except for calculus in which I received a C by dint of hard work. Mine is not a math brain. But then again, my college majors didn't require any more math if you'd taken calculus, so I haven't done much math beyond calculating tips etc. since highschool, which probably explains a lot.

and I still got a 640 the first time and a 500ish the second time on the math part of the GRE. Go me!

Comments

[forvrin.livejournal.com]

Simpler equation would be

1.0825x = 8

x = 8 / 1.0825

x = 7.3903

[telophase.livejournal.com]

Hee, thanks. See, this is why I'm in the fluffy sciences, not the hard sciences. :D

[llamameeljueves.livejournal.com]

That's the perfect way. So every time you want to calculate the "real price" (w/o th tax), use this formula:

Real price = round number divided by (1 + Sales taxes)

Or in few words:

Price = Taxed value / 1.0825

many small steps

[solarbird]

Okay! So:

X + X*0.0825 = 8

is the same as

X*1 + X*0.085 = 8

...because X = 1*X = X*1. Try this for any number X if you want to. Doing things for yourself like this helps, srsly.

X*1 + X*(0.085) is the same as
X*(1+0.085)

...because you can factor out X, which will hopefully look familiar to you.

Since 1.0.085 = 1.085, This reduces further to:

X*(1.085) = 8

So if you divide both sides by 1.085, you get:

X*(1.085)/(1.085) = 8/1.085

And anything divided by itself (except 0) = 1, so:

X*1=8/1.085

And X*1 is just X, so:

X=8/1.085

Notice that we haven't changed the 8 at any point, or even really done anything to it. So you can put any number in its place to get the "real" price for the post-tax replacement.

Does that help?

Re: many small steps

[solarbird]

I swear when I started that reply there were no other replies.

Re: many small steps

[telophase.livejournal.com]

I believe ya. :D But I shall keep the explanation and look at it intently, because it really rather bothers me that I don't remember the steps involved in doing an equation this simple, and I probably can't always rely on Livejournal to be there for me. :D

Plus, it will keep my mother, the retired math teacher, from mocking me. :D

Re: many small steps

[solarbird]

I made a typo, foo. I wrote:

Since 1.0.085 = 1.085, This reduces further to:

It should have been this:

Since 1+0.085 = 1.085, This reduces further to:

to wit: oops, sorry