Is this math impossible?

April 14, 2011 7:46 PM

I do not know math. I have a number, and I want to backwards engineer that number so I can arrive at it by adding some unknown amount and 13% of that unknown amount. Is there any way to figure this out besides trial and error?
posted by aunt_winnifred to Science & Nature (6 answers total)

Best answer: y is your number.
x is your unknown number.
x+.13x=y
1.13x=y
x=y/1.13

You can get your unknown number by taking the number you want to arrive at and dividing by 1.13
posted by yeolcoatl at 7:48 PM on April 14, 2011

Best answer: Yes. You need algebra.
Let your unknown amount be x. Then the unknown amount plus 13 % of your unknown amount is x + 13 % x
= x + 0.13 x
= 1.13x
We want this to be equal to the number you have. Therefore, 1.13x = your number and x = (your number)/1.13. That's your answer.
posted by peacheater at 7:50 PM on April 14, 2011

Best answer: Let your number be k and x be the unknown amount.

You want k = x + 0.13*x.

Now just solve that equation:

k = x + 0.13x
k = 1.13x
k/1.13 = x

In other words, divide your number by 1.13 to get the unknown amount.

On preview, yeolcoatl is exactly correct but I've included my explanation just in case it helps.
posted by yaymukund at 7:50 PM on April 14, 2011

Response by poster: thank you metafilter.
posted by aunt_winnifred at 7:59 PM on April 14, 2011 [3 favorites]

I am putting this here for others who might read this and ask why someone would ever want to know this math.

This question demonstrates exactly how we work with sales taxes. In this case, you know the total price that was paid and you know that the sales tax rate was 13%. The formulas above show how to do the math to figure out how much the item originally cost.

Also applies to discounts/markups, trying to figure out the old price before it was marked up 13%.
posted by CathyG at 7:29 AM on April 15, 2011 [1 favorite]

Math is all of

1. necessary
2. possible
3. fun
posted by rhombus at 10:38 AM on April 15, 2011 [1 favorite]