Subject: MATH PROBLEM From: Jeep man Date: 24 Feb 02  05:45 PM This has naught to do with music,but I think Mudcatters will not mind. How to figure sales tax on a set amount which has the tax included? Example, Selling price, $100. Tax in NC is 6.5%. There is a simple formula for figuring the exact selling price and the tax. Help anyone? Jeep To explain, I just spent 3 days at a Bluegrass festival helping a friend at his booth. (Music Store). We sold everything "Tax Included". Get the picture? Jim 
Subject: RE: BS: MATH PROBLEM From: MudGuard Date: 24 Feb 02  05:55 PM total = price + (price * 6.5)/100 or total = price * 1.065 ==> price = total / 1.065 tax = price * 0.065 HTH MudGuard 
Subject: RE: BS: MATH PROBLEM From: Sorcha Date: 24 Feb 02  05:56 PM Aww shit.....math. It is easy, but my pore ole brain can't remember....... 
Subject: RE: BS: MATH PROBLEM From: GUEST Date: 24 Feb 02  05:59 PM That is so simple, I can't even be bothered explaining it. HINT: Switch on your brain and think for a few minutes. I'm sure, unless you're dyspraxic, that you'll be able to work it out for yourself. 
Subject: RE: BS: MATH PROBLEM From: Sorcha Date: 24 Feb 02  06:03 PM Well, then, honeychile, Iz dyspraxic. Thanks for letting me in on the secret. 
Subject: RE: BS: MATH PROBLEM From: Jeri Date: 24 Feb 02  06:04 PM It's beyond me, but with MudGuard's formula, aren't you subtracting 6.5% of 100, which isn't what 6.5% of a lesser amount (the sale price you added it to) would be? I mean, you don't need to know what 6.5% of 100 is.
100 = X + (X * .065) 
Subject: RE: BS: MATH PROBLEM From: GUEST Date: 24 Feb 02  06:12 PM Jeez, Multiply (that's the X button on your calculator)the selling price by .935 and you'll get the nontaxable portion. If you can master addition and subtraction, you shouldn't have difficulty with the rest.

Subject: RE: BS: MATH PROBLEM From: Pene Azul Date: 24 Feb 02  06:19 PM GUEST's solution is incorrect. Use Mudguard's method of dividing the total by 1.065 to find the price. Then you can subtract that from the total to find the tax, or as Mudguard said, you can multiply it by .065 to find the tax. Jeff 
Subject: RE: BS: MATH PROBLEM From: Jeri Date: 24 Feb 02  06:20 PM Again, that's 100  6.5% You come up with (duh) 93.5 This is 100  6.5% of 100
The 93.5% is supposed to be the selling price. GUEST, you're not doing better than anyone else.

Subject: RE: BS: MATH PROBLEM From: John Routledge Date: 24 Feb 02  06:24 PM If you multiply selling price by .935 you get the price on which 6.5% tax is paid to give the selling price inclusive of tax The use of "nontaxable portion" by guest is potentially confusing as it is actually this amount that is subject to tax. Cheers  Happy Calculating 
Subject: RE: BS: MATH PROBLEM From: Jeri Date: 24 Feb 02  06:25 PM GACK! MudGuard did get it. I only had to read it 3 or 4 times. I will go sit in a corner now.

Subject: RE: BS: MATH PROBLEM From: Sorcha Date: 24 Feb 02  06:45 PM Come join me, Jeri. I'm already there. What are you drinking tonight? I'll buy......... 
Subject: RE: BS: MATH PROBLEM From: John Routledge Date: 24 Feb 02  06:47 PM Thanks Jeri and MudGuard I reread MudGuard's post and he got it right first time. Cheers MudGuard  John

Subject: RE: BS: MATH PROBLEM From: McGrath of Harlow Date: 24 Feb 02  06:51 PM Our Value Added Tax is 17.5%. They'd never have dared to do that to us in the days of pounds shillings and pence, and no pocket calculators. 
Subject: RE: BS: MATH PROBLEM From: M.Ted Date: 24 Feb 02  06:59 PM As a bit of advice, calculate your price *beforehand*it looks like you were trying to save trouble, but it hasn' turned out that waythe problem is, how much did you sell things for? Was the price $100, or was $100 the sum of the price and 6.5% of the price? The amount of tax that you owe will be slightly different Your problems will not be over then, simply because it is often the case that, rather than being a straight percentage, the amount of tax was rounded off in a prescribed way by the stateto make this easy, the state provides a table of the tax surcharges that you are obliged to collectand they expect you to collect them as per their formulayou better have your friend talk to his accountant about how to handle this all, because, take it from me, the State of North Carolina will not think much of the idea that you calculated what you owe them based on a formula that came from an internet discussion thread 
Subject: RE: BS: MATH PROBLEM From: Jon Freeman Date: 24 Feb 02  07:34 PM The simplest way to think of this is that to add tax, you multiply by 1 + the % tax expressed as a decimal. For example, to add 17.5% (wich is 1 + .175) VAT on £10 you get 10 * 1.175 = £11.75. To reverse this processess, you simply divide, i.e. £11.75 / 1.175 = £10 Jon 
Subject: RE: BS: MATH PROBLEM From: GUEST Date: 24 Feb 02  07:39 PM Clear, simple and accurate, Jon Thank you 
Subject: RE: BS: MATH PROBLEM From: SINSULL Date: 24 Feb 02  07:50 PM Is this lack of Mathematical ability another reason folkies can't make a dime? 
Subject: RE: BS: MATH PROBLEM From: Jon Freeman Date: 24 Feb 02  08:45 PM Thanks guest, hope that "rule" of how you added may have helped others see Mudguard's solution. My own inclination would be follow Jeff's subtraction, e.g if Jeepman was constructing a spread sheet for his sales, it may make sense to have some cell containing the percentage tax,  I'll call it T1. On a spreadsheet that works like Excel, we could have: Cell T1  the actual % tax (useful as if tax ever changed, onlt the one cell would have to be changed):
Row1  headings
row 2 and subsequent rows  actuals and formulae Just copy formulae down a few rows and add a few totals... Jon 
Subject: RE: BS: MATH PROBLEM From: Jon Freeman Date: 24 Feb 02  08:47 PM opps, for all my references to row 1 in row 2 except the one with the $ sign, read 2!!! Jon I think I put 2s in appropriate places. JoeClone 
Subject: RE: BS: MATH PROBLEM From: Jeep man Date: 24 Feb 02  09:06 PM Thanks, folks. If the combined knowledge of all Mudcatters was put to use, we could probably end all wars, eliminate hunger and desease, and everyone would pick and sing in tune. Mucho thanks, Jeep 
Subject: RE: BS: MATH PROBLEM From: 8_Pints Date: 24 Feb 02  09:17 PM Who said there are three kinds of mathematician: those can count and those who can't! *BG* Bob vG 
Subject: RE: BS: MATH PROBLEM From: harpgirl Date: 24 Feb 02  09:36 PM What you do is find what 6.5% of 100 would be. You then minus that from a 100. You would get $93.50 without tax or n times .065cents That's how you would get the taxes for that state. This is from Nathan, harpgirl's son... and if you need help with any other math problem contact me at nated2000@yahoo.com and I will get back to you as soon as possible. 
Subject: RE: BS: MATH PROBLEM From: IvanB Date: 24 Feb 02  10:47 PM No, Mudguard's solution is the correct one. If you sell something for $100, sales tax included, the actual selling price is 93.90 (100/106.5). The tax at 6.5% would be $6.10. I've done sales tax reports in Michigan and I know here that, no matter how much you collect by using the state's tax tables, you send in 6% of your sales at the end of the month. 
Subject: RE: BS: MATH PROBLEM From: Bobert Date: 24 Feb 02  11:07 PM If a hen and a half can lay an egg and a half in a day and a half... then how long would it take a monkey with a wooden leg to kick the seeds out of a dill pickle???... You all wore this ol' hillbilly out tonight with all this mathmatics... Had to give the Wes Ginny slide rule a couple of asprins, too. 
Subject: RE: BS: MATH PROBLEM From: AR282 Date: 24 Feb 02  11:21 PM Multiply the selling price by .065 and then add that amount to the selling price. 
Subject: RE: BS: MATH PROBLEM From: Gary T Date: 25 Feb 02  12:09 AM MudGuard's explanation is correct. IvanB's figures are correct. GUEST at 24Feb02  06:12 PM, John Routledge, and Nathan (harpgirl's post) were wrong. Problem stated that selling price INCLUDING tax was 100, thus "item price + 6.5% of item price = 100". Whatever item price is, it is NOT 100, and thus 6.5% of item price is NOT 6.5. AR282's reply is wrong if he uses MudGaurd's definition of "selling price" (item price plus tax). It could be considered technically correct if he means the pretax price of the item, but is then useless in solving the problemwe already know how to figure the tax given the item price, the question is how to figure the item price. To sum it up in algebra: P = item price, what we're trying to calculate S = amount of sale (MudGaurd's "selling price"), which includes item price plus tax, which is 6.5% of item price S is known to be 100. What is P? S = P + 6.5%P = 100 S = 1.065P = 100 1.065P = 100 P = 100/1.065 = 93.90 (rounded to second decimal place) Double check (all figures rounded to second decimal place): 93.90 + 6.5%(93.90) = 93.90 + 6.10 = 100 Figures add up, all is well. 
Subject: RE: BS: MATH PROBLEM From: JohnInKansas Date: 25 Feb 02  02:21 AM An amazing amount of discussion, for an apparently trivial question. About the only thing "proved" is that the first GUEST was wrong  for a bunch of musicians, it ain't that simple. MudGuard's answer is correct. The only simplification I can see is to "reduce" the 1/(1+.065) to 0.93897. Multiply the amount "collected" by 0.93897 to get the "sale price." Then when the "sale price" is multiplied by 0.065, you get the tax. Add Price + Tax and you should come up with the amount collected ($100 for purposes of the original question. The remaining difficulty is that various tax jurisdictions don't always come up with the "mathematically correct" number as the amount you must pay. Many tax jurisdictions will permit you to pay a "lump sum" percentage of the total "amount of sales." Others insist that each item sold must be taxed separately, and you must pay the "total of the taxes collected on individual sales." Some of these later For information on North Carolina, you might want to check out: Tax Forms and Instructions: North Carolina From there, you can click to: Sales and Use Taxes: North Carolina The "real world answers" should be there(?). John 
Subject: RE: BS: MATH PROBLEM From: Pene Azul Date: 25 Feb 02  02:29 AM According to the tax table on their site (http://www.dor.state.nc.us/downloads/E502G_102.pdf), the tax on an individual sale is conventionally rounded off to the penny. Jeff 
Subject: RE: BS: MATH PROBLEM From: JohnInKansas Date: 25 Feb 02  03:17 AM Jeff I didn't go into the NC tax tables  just thought it a good idea for the ones with the problem to go to the source. I have run into places where "rounded off to the penny" actually meant "rounded up to the penny." If the "calculated" tax was 5.01 cents, you paid 6 cents. Places with this kind of "math" seem often to demand that each individual sale be reported separately, since  on average  it gets them an extra halfcent per sale(?) Usually, math works; but when dealing with politicians, it's best to check the "official" sources. John 
Subject: RE: BS: MATH PROBLEM From: GUEST,bradfordian Date: 25 Feb 02  06:42 AM If sales tax is 6.5%, then you can use the following fractions: For tax 13/213, for cost of item less tax 200/213. In UK (17,5%) tax = 7/47 & price less tax = 40/47 Hopefully!!! Check these out for $10.65 & £11.75 respectively. 
Subject: RE: BS: MATH PROBLEM From: bradfordian Date: 25 Feb 02  06:46 AM oops. cookie now reset 
Subject: RE: BS: MATH PROBLEM From: GUEST,Nigel Date: 25 Feb 02  08:32 AM Bradfordian's solution is correct. My wife is a VAT auditor (makes sign of cross and checks garlic necklace) and she has been given these same fractions to use. McGrath, 17½% is a doddle to use, (purchase price plus 10% plus half as much again plus half as much again). Musically speaking (back to subject) think of it as 10% with a double dot. Before decimalisation, 7/48 would have been a simpler fraction, (7pennies in 4 shillings, or 35 pennies[2/11d] in the pound!) 
Subject: RE: BS: MATH PROBLEM From: Jon Freeman Date: 25 Feb 02  09:08 AM Thinking of rounding, when using computers, one needs to be sure of the rounding method used. Excel uses conventional rounding but I have run into programs Deplhi springs to mind  where the round function works on bankers rounding which handles a final 5 in the decimal portion differently by rounding by towards the nearest even number (I think) so Excel would give:
Round(2.5,0) = 3 but using Delphi, you would get:
Round(2.5) = 2 Jon 
Subject: RE: BS: MATH PROBLEM From: M.Ted Date: 25 Feb 02  09:48 AM This is not a mathematical problem, it is a tax problem! JohninKansas (a man of many resources, and much practical knowledge) has linked you to the appropriate downloadable sales tax tablesall of you math whizzes, take notice! If the "6.5%" sales tax table applies (In some counties, it is 7%) when the taxable amount is from $0.850.99, you are obliged to collect $0.06, but from $1.00 to $1.07, you collect $0.07multiply everything out, subtract, and then just put on a fake mustache and beard and do all transactions in cash 
Subject: RE: BS: MATH PROBLEM From: Mary in Kentucky Date: 25 Feb 02  10:07 AM Nathan, this problem is not as straightforward as it first appears. The hardest part for me was understanding the original question. I worked in a lab where we had to calculate the amount of surfactant in a resinous emulsion, and it was the same type of problem. You know what the total weight should be, and you know what percentage of surfactant to one of the parts should be. It's just not a straightforward percent problem. As a matter of fact, I noticed two groups of people and how they calculated this, the Mudguard type (which includes me) and the Jon Freeman type (the engineers). Mudguard sets up an equation and solves for the unknown. Jon multiplies and divides, a sequential type thinking as opposed to the other wholistic type thinking. I observed that the people trained as engineers did this kind of calculation so much that their thought patterns were established to do it the fastest way. Also, one engineeringschooltrained guy used an ancient HewlettPackard calculator that required him to enter the numbers, then enter the function to perform. We joked that the best way to hide an invention was to put it in a patent for everyone to read. The descriptions of amounts of materials used are so convoluted and hard to interpret, it's hard to duplicate the process. 
Subject: RE: BS: MATH PROBLEM From: Mary in Kentucky Date: 25 Feb 02  10:15 AM I meant to say operation instead of function. 
Subject: RE: BS: MATH PROBLEM From: Dave the Gnome Date: 25 Feb 02  10:22 AM Working tax out is dead easy! Just follow the instructions on the tax inspectors letter. a) Work out how much you earned and b) Send it to the tax office... Hope this helps ;) Cheers Dave the Gnome 
Subject: RE: BS: MATH PROBLEM From: Mary in Kentucky Date: 25 Feb 02  10:44 AM Did you ever notice that THE IRS spells THEIRS? 
Subject: RE: BS: MATH PROBLEM From: IvanB Date: 25 Feb 02  11:34 AM Looking at the NC Sales & Use Tax report, it specifically states that the sales price should be the amount of gross sales without sales tax included. Therefore Jeep's friend needs a method to calculate the selling price before tax. That's exactly what Mudguard gave. As far as the 'charts,' the NC chart states on the bottom that it is provided 'as a convenience to retailers' to help them figure out how much to collect on various sale amounts. The only connection the charts have to the ultimate reporting and paying of sales tax collections is that, if they are used, the retailer should be in the ballpark of the required amount when the report is filed. When the Semimonthly tax report is filled out, it's the gross amount of sales for the period that counts and not the individual sales and the 'chart' amounts of tax on them. If you overcollect (which is almost guaranteed when the charts are used), you report the overcollection amount on a separate line of the tax form and include it with your payment. If you undercollect, you're SOL, 'cause you still gotta pay the 6.5%. 
Subject: RE: BS: MATH PROBLEM From: GUEST,Lyle Date: 25 Feb 02  02:53 PM Not too bad, folks, BUT I just gave this problem to a group of 5th graders I'm working with, and 23 out of 24 got the right answer in about 2 minutes. 
Subject: RE: BS: MATH PROBLEM From: John Routledge Date: 25 Feb 02  03:23 PM Did they have as much fun though pondering the meaning of life and taxation as we know it? 
Subject: RE: BS: MATH PROBLEM From: Mrs.Duck Date: 25 Feb 02  03:30 PM $100 = 106.5% price $100/1.065 = price price = $93.90 Not saying anything new just summarising for my brains sake. 
Subject: RE: BS: MATH PROBLEM From: Mr Red Date: 25 Feb 02  04:31 PM Dyscalculia Anonymouse Anyone? what is dyspraxis anyway  SOED CD ROM don't know! 
Subject: RE: BS: MATH PROBLEM From: JohnInKansas Date: 25 Feb 02  05:27 PM The Random House Unabridged Dictionary  CD ROM version defines dyspraxia as the "inability to perform coordinated movements." John 
Subject: RE: BS: MATH PROBLEM From: harpgirl Date: 25 Feb 02  09:38 PM Okay Mary. I got a couple math problems for you. 1.find the vertex of x(squared)2x+36 if the vertex is (b/2a) 2.what is the slope if you have (3,2) for the first pair and (1,2) for the second pair. 3.find the number of moles if you have 12.04x10(to the 24) because big poppa pump is your hookup, holla if you hear me, your pal ja killer aka nathan dollar 
Subject: RE: BS: MATH PROBLEM From: Louie Roy Date: 26 Feb 02  12:58 AM Jeep Man you have received a number of ways to do this simple problem and the way I was taught when I was in the 5 th grade in 1934 and of course at that time there was no computer or calculators it was a done with a pencil and paper.I'll use your problem $100 tax included.You take $ 100 and divide it by 1.065 and that gives you an answer of $93.89673 round this off to 93.90.Now take 93.90 and times this by .065 this give you a figure of $ 6.1035 round this off to $6.10 Add 6.10+93.90 =100.It works the same long hand only a lot slower.Long hand you would start with 100 divided by 1.065 and since to divide with 1.065 you have to move the decimal point 3 places to the right so now you would have 100000 divided by 1065 if you divide this out you will find the answer is the same Louie Roy 
Subject: RE: BS: MATH PROBLEM From: Trevor Date: 26 Feb 02  08:04 AM If you turn the percentage figure into a vulgar fraction (cue for gags!), add the top number (I can't remember whether that's the numerator or denominator) and the bottom number together. That gives you the new bottom number, and the top number stays the same. This will then give you the fraction that has to be deducted from the tax inclusive price to calculate the taxless price. Eg Tax free price 1.00 25% tax (ie 1/4) 1.25 To work it back, 1+4 = 5, top number stays the same, therefore deduct 1/5. Lo and behold 1.25  1/5 =1.00. So in your problem deduct 6.5/106.5. Clear as mud eh? 
Subject: RE: BS: MATH PROBLEM From: Mary in Kentucky Date: 26 Feb 02  08:42 AM Nathan, I can't holler 'cause I have no idea what you're talking about! Also, you're straining my poor ole brain...but since you were a good sport, I'll give it a try (without any referece books). 1) 1 (or 1,35 I forgot what the vortex is) 2) slope is 0, a horizontal line 3) 20 
Subject: RE: BS: MATH PROBLEM From: Jon Freeman Date: 26 Feb 02  09:45 AM Mary, I think the vertex is the highest or lowest point. I seem to remember using differentation to solve these so..
y = x^2  2x + 36 at the turning point, dy/dx = 0 so
2x  2 = 0
substituting for x... I hope thats right... that was about as far as I got with maths before walking out of school and it was a long while ago... Jon 