How do I calculate how much (x) is needed so that $x = zx + zy$?

48 Views Asked by Bumbble Comm At 31 Mar 2026 - 9:10

I have y units and want to know how many extra units need to be created so that the extra units match a given percentage of the total units.

Example:

I have 100 units. I want to create x amount of units until x is equal to 1% of 100 + x. How much x do i need to create?

There are 2 best solutions below

Bumbble Comm On 10 Sep 2020 - 6:27 BEST ANSWER

So I think the problem is interpreted as you have $y$ units initially and you want to make $x$ more units until $x$ is $100z$% of $x+y$.

This gives the equation you provided, $x=zx+zy$. We can combine the $x$'s on both sides to get $x(1-z)=zy$, so $x=\frac{zy}{1-z}$

Bumbble Comm On 10 Sep 2020 - 5:40

"I have 100 units. I want to create x amount of units until x is equal to 1% of 100 + x. How much x do i need to create?"

You want x= 0.01(100+ x)= 1+ 0.01x. Subtract 0.01x from both sides- 0.99x= 1 so x= 1/0.99= 100/99= 1.010101... where "01" repeats.

Check: with x= 100/99, 100+ x= 9900/99+ 100/99= 10000/99. 1% OF that is 100/99= x.