find x and y when you know the % of one from the other

[EdB]

Hi

I'm wondering if it's possible to work this equation backwards, here is what I have

x - (y * 2) = z

I know Z. I also know y is 12.3% of x. Is it possible to find x and y?

Here are 2 examples

699 - (86 * 2) = 527
I know z (527). I know that y (86) is 12.3% of x (699)

899 - (111 * 2) = 677
I know z (977). I know that y (111) is 12.3% of x (899)

Knowing z (the final answer) and knowing y is 12.3% of x is there a calculation I can do to find x and y?

Many thanks
Ed

 

[Ishuda]

Hi

I'm wondering if it's possible to work this equation backwards, here is what I have

x - (y * 2) = z

I know Z. I also know y is 12.3% of x. Is it possible to find x and y?

Here are 2 examples

699 - (86 * 2) = 527
I know z (527). I know that y (86) is 12.3% of x (699)

899 - (111 * 2) = 677
I know z (977). I know that y (111) is 12.3% of x (899)

Knowing z (the final answer) and knowing y is 12.3% of x is there a calculation I can do to find x and y?

Many thanks
Ed

If y is 12.3% of x than what is the formula for y in terms of x? Given that, substitute that formula into your equation for the y part and that will give you an equation for x in terms of z. Since you know z, you can compute x, and then compute y.

Example: y is 10% of x, z is 700 and
x - 5 y = z.
Since y is 10% of x
y = 0.10 x
so
x - 5 * (0.10 x) = 700
or
x - 0.50 x = 0.50 x = 700
or x = 1400.
y = 0.10 x = 0.10 * 1400 = 140

 

[EdB]

An example:
z = 345, y = 15.5% of x

x - 2y = 345
x - 2(.155x) = 345
x - .31x = 345
.69x = 345
x = 345/.69 = 500

Hi Denis

Many thanks for this!
I understand up to the point of .69x = 345
Where is .69 coming from?

Many thanks again

 

[ksdhart]

The .69x comes from doing the subtraction at this step \(\displaystyle x\:-\:.31x\:=\:345\). Because there are two terms with the same variable, we can subtract the coefficients (the numbers in front of the variable).

If it makes it any clearer, you might think of it as \(\displaystyle \frac{100}{100}x-\frac{31}{100}x=345\). Then after subtracting, you'd have \(\displaystyle \frac{69}{100}x=345\) or \(\displaystyle .69x=345\)