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### Finding Original Amount before a Percent Was Added

```Date: 04/24/2007 at 11:36:13
From: Sytolli
Subject: tax percentage

I paid \$25.00 for gas.  The cost included 42% in tax.  What is the
cost of the gas without the tax?

I multiplied 42% by \$25.00 and subtracted the result from 25, but this
answer is not appropriate.  I think I am missing a step.

```

```

Date: 04/24/2007 at 12:56:18
From: Doctor Ian
Subject: Re: tax percentage

Hi Sytolli,

Here's one way to think about it.  For every \$1 you pay for gas, you
pay \$0.42 in tax, right?  That is, \$1 worth of gas costs you \$1.42.

Let's call that one 'unit' of gas.  How many units can you buy for
\$25?  That would be

25
---- = 17.6
1.42

That is, you can buy 17.6 units of gas for \$25.  Each of those units
contains \$1 in gas, and \$0.42 in tax.  So the price without tax would
be 17.6 dollars, or \$17.60.

Does that make sense?  Let me know if you need more help.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/

```

```

Date: 04/24/2007 at 14:28:31
From: Doctor Riz
Subject: Re: tax percentage

Hi Sytolli -

Just a quick follow up on Dr. Ian's comments to show you a slightly

Let g be the cost of the gasoline before the tax.  Then, since you pay
42% of that amount in tax, the amount of tax is .42g.  That means the
total amount you paid is g + .42g or 1.42g.  Since the total was \$25,
we can say that:

1.42g = 25

Dividing both sides by 1.42, we get g = 17.6, so the cost of the gas
before taxes was \$17.60.

Note that this approach works exactly the same as Dr. Ian's, with the
1.42 representing the "actual cost" of each dollar of gasoline.

- Doctor Riz, The Math Forum
http://mathforum.org/dr.math/

```

```

Date: 04/25/2007 at 13:14:26
From: Sytolli
Subject: Thank you (tax percentage)

Doctors Ian and Riz,

Thank you for your replies.  I knew there was a simpler way to look at
it and just couldn't figure it out.  It makes a lot of sense.  Your
help is much appreciated.
```
Associated Topics:
Middle School Algebra
Middle School Ratio and Proportion

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