Solve for x: x = [1000000 x 12% + (4500000 - 1000000 - 100000 - 50000 - x - 1000000) x 10%] x 80%.

Step-by-step solution

1. 1

   Rewrite the percentages as decimals. Percentages are only a notation for hundredths, and decimals are easier to distribute:

   $12\%=0.12,\qquad 10\%=0.10,\qquad 80\%=0.80$

2. 2

   Simplify the inner bracket, keeping the $-x$. Add up only the numbers:

   $4500000-1000000-100000-50000-1000000=2350000$

   so the inner bracket is $2350000-x$. The unknown stays inside; that is exactly why this is not a one-step problem.

3. 3

   Evaluate the fixed part and distribute the 10%.

   $1000000\times 0.12=120000,\qquad 0.10(2350000-x)=235000-0.10x$

   The outer bracket is therefore $120000+235000-0.10x=355000-0.10x$.

4. 4

   Apply the outer 80%. Multiply both terms:

   $x=0.80(355000-0.10x)=284000-0.08x$

   Note $0.80\times 0.10=0.08$: the two percentages compound, they do not add.

5. 5

   Collect the $x$-terms. Adding $0.08x$ to both sides puts every $x$ on the left:

   $x+0.08x=284000\quad\Longrightarrow\quad 1.08x=284000$

6. 6

   Divide and check.

   $x=\frac{284000}{1.08}=262962.962\overline{9}$

   Substituting back: $2350000-262962.96=2087037.04$, times $0.10$ is $208703.70$, plus $120000$ is $328703.70$, times $0.80$ is $262962.96$ — the same $x$ we started from. $\checkmark$