Q:

Splitting money to equal values after different tax rates

Sorry if the format of this question is slightly off I’m not a regular user but need help.  
I have Money of £704000. 
This needs to be split between two people A and B equally after tax
A has tax rate of 11.75% 
B has tax rate of 23.5% 
How would I go about solving this? 

A:

Let's build this from the ground up.  We want to split an amount of $704~000$ to A and B so that after their taxes have been deducted, they both get the same amount $x$. 
Let's first imagine that we split the amount into two boxes, without deducting any taxes. 
$$\tag{1}
704~000 = A + B
$$
$A$ is the part that will go to A and $B$ is the part that will go to $B$. Now let's think about the taxes.  If A has the amount $A$ before the taxes, how much is there after taxes?  We know that A's tax percentage is $11.75~\%$. That means that after the deduction, A will have
$$
\underbrace{A}_{\text{original amount}} - \underbrace{0.1175 A}_{\text{taxes}} = A(1-0.1175) 
$$
So this is what A will get after the taxes and this should be equal to $x$. So we know
$$
A(1-0.1175) = x \qquad \Rightarrow \qquad A = \frac{x}{1-0.1175}
$$
This was pure algebra. 
Next, we do the same thing for B. He also has to to pay taxes, so the amount after taxes is 
$$
B - 0.235B = B(1-0.235) = x \qquad \Rightarrow \qquad B = \frac{x}{1-0.235}
$$
Now we have alternative expressions for $A$ and $B$, and we can plug them into Equation ($1$):
$$
\begin{split}
704~000 &= \frac{x}{1-0.1175} + \frac{x}{1-0.235}\\
&= \left( \frac{1}{1-0.1175} + \frac{1}{1-0.235} \right) x \\
&\approx (1.1331 + 1.3072)x \\
& = 2.4403 x
\end{split}
$$
Dividing both sides by $2.4403$, we get
$$
x = \frac{704~000}{2.4403} \approx 288~485.1
$$

Answer: both get approximately $288~485.1$ pounds.