Calculating a Percentage

[Tigers198743]

Can anyone explain the mathematical theory behind the following equation?

If your purchase price is $100 and you're expecting a 2% reduction, what is the purchase price?

Is it either

$100 - (.02 * $100) = $98

or

$100 / 1.02 = $98.04

and why?

Thank you

 

[Deleted member 4993]

Can anyone explain the mathematical theory behind the following equation?

If your purchase price is $100 and you're expecting a 2% reduction, what is the purchase price?

Is it either

$100 - (.02 * $100) = $98

or

$100 / 1.02 = $98.04

and why?

Thank you

How much did you pay after 2% reduction?

 

[HallsofIvy]

Can anyone explain the mathematical theory behind the following equation?

If your purchase price is $100 and you're expecting a 2% reduction, what is the purchase price?

What is your understanding of "2% reduction"? 2% of what?

Is it either

$100 - (.02 * $100) = $98

IF the "2% reduction" is 2% of the "purchase price" then, yes, 2% of $100 is $2. With a $2.00 reduction, the new price is $98.

or

$100 / 1.02 = $98.04

and why?

If the 2% is of the new price, then P=100- 0.02P so that 1.02P=100 and P= $100/1.02= $98.04. But frankly, that makes no sense to me!

Thank you

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[Dr.Peterson]

Can anyone explain the mathematical theory behind the following equation?

If your purchase price is $100 and you're expecting a 2% reduction, what is the purchase price?
Is it either
$100 - (.02 * $100) = $98
or
$100 / 1.02 = $98.04
and why?

Was this the exact wording of a problem you were given? As written, it makes no sense: It tells us that the purchase price is $100, so that's the purchase price! What you expected is irrelevant.

If you wrote this yourself, you'll have to clarify what quantities you are referring to. For example:

• If the normal price is $100 and you get a 2% reduction in price because of your special privilege, what do you actually pay? The answer to that question would be 100*(1 - 0.02) = $98.
• If, after a 2% reduction in price, you pay $100, what is the price before the reduction? Then the answer is 100/(1 - 0.02) = $1.02.
• There are several other questions you could be asking; your second answer would be correct for some of them, but the wording would have to be different.