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How Much of a Total Price Is the Tax?

```Date: 10/20/2003 at 08:01:59
From: Tracey
Subject: working out the vat content of an amount

How do you work out the VAT content of an amount? Eg: £55?

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Date: 10/22/2003 at 09:17:02
From: Doctor Peterson
Subject: Re: working out the vat content of an amount

Hi, Tracey.

differently in America, showing the actual price in a store and
adding the tax to that when it is bought. To find the VAT when you
know only the final amount you paid, you need a little algebra.

You don't know the actual price of what you bought, so call it X. You
do know the tax rate (but I don't!); I'll call it r. (For example, if
the tax rate is 15%, then r=0.15.)

Then the amount you pay is

X + rX = (1+r)X

If you know you paid Y, then you have to solve the equation

Y = (1+r)X

for X, which you do by dividing by 1+r:

Y
X = -------
(1 + r)

Finally, since you want not the original price, but the amount of tax
you paid, you have to multiply this by r:

r
tax = rX = ------- * Y
(1 + r)

So, for example, if the tax rate is 15%, you find the tax by
multiplying the total price by (0.15)/(1.15) = 0.1304

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
Elementary Fractions
Middle School Fractions

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