1

I need help for one question, I don't know if this is a percentage reverse, sorry if is the wrong name. The question is: I need increase a specific value in a percentage that I don't know to reach another value then apply exactly $30$ percent to reduce to original value, like this example: $950$ is original value I need increase it to a value, in this case I know is $1358.50$ then I apply a discount of and back to $950$ The question is I tried a lot of times until reach this. I need a formula to do the right way and don't make mistakes with the exactly value even cents. Thank you

JohnColtraneisJC
  • 1,919
Igor
  • 11
  • To clarify: you have a starting price $X$ and you are asking for a new price $Y$ such that a $30%$ discount from the price of $Y$ will get you back to $X$? – lulu Aug 18 '17 at 00:21
  • Just to say, a $30%$ discount from a price of $1358.50$ does not get you to $950$. It's close, but it only gets you to $950.95$. A better value for $Y$ in this case would have been $1357.14$. – lulu Aug 18 '17 at 00:23
  • Well, I'm not at all sure my interpretation of your question is correct. But on the chance that it is: You are asking for $Y$ such that $.7\times Y=X$. Thus you just want $\frac X{.7}$. Note that $.7 = 1 - .3$ and $\frac {950}{.7}\approx 1357.14$. – lulu Aug 18 '17 at 00:32
  • Exactly like you said lulu, yes I know that amount isn't return to exact 950. This is my big problem, because need to be exact. – Igor Aug 18 '17 at 00:32
  • Lulu, That's it! Perfect! Thank you very much! – Igor Aug 18 '17 at 00:39
  • 1
    Great! If you don't mind, could you accept the answer I posted below? The site doesn't like it if questions go without accepted answers. – lulu Aug 18 '17 at 00:41

2 Answers2

2

If the starting price is $X$ then you seek a new price $Y$ such that a $30\%$ discount from $Y$ gets you back to $X$. Thus you are asking $$(1-.3)\times Y = X\implies Y= \frac X{1-.3}=\frac X{.7}\approx 1.42857\times X$$

Note that starting with $X=950$ we get $Y\approx 1357.14$ which is close to the value you wrote.

Note too that if you had a discount amount other than $30\%$ you would just change the $.3$ accordingly. Thus if the desired discount was $17\%$ you'd just have $Y=\frac X{1-.17}$.

lulu
  • 70,402
0

Basically you want $(1 - .30)*(1 + x) ORIGINAL = ORIGINAL$

Or $.7(1+x) = 1$

Or $(1+x) = \frac 1{.7} = 1.4286$

Or $x = .4286 = 42.9\%$

So the price you raise it to is $1.4286*950 = 1357.55$

And $70% of 1357.55 = 950.285$

Which is off but $28 \frac 12$ cents.

To be exact you want $\frac 1{.7} = \frac {10}{7} = 1 \frac 37 = 1.42 + \frac 6{700}$ so you want $42 \frac 67\%$.

Then $(1.42 + \frac 6{700}) 950 = 1357.14 \frac {3}{100}$

$.7*135 *1357.14 \frac {3}{100}=950$

But you'll go crazy chasing pennies.

fleablood
  • 124,253