Solve for x: (3669724.77 - x) times 3% plus 13% of x equals 330275.23.

Step-by-step solution

1. 1

   Convert both percentages to decimals first. A percent is a hundredth, so $3\%=0.03$ and $13\%=0.13$:

   $0.03(3669724.77-x)+0.13x=330275.23$

   The structure is the classic "split a total between two rates" equation: an amount $x$ is taxed at the higher rate and the remainder at the lower one.

2. 2

   Distribute the 0.03 across the bracket.

   $0.03\times 3669724.77=110091.7431$

   $110091.7431-0.03x+0.13x=330275.23$

   Note that $x$ appears twice with opposite signs, so the two terms must be combined before anything else.

3. 3

   Combine the two $x$ terms.

   $-0.03x+0.13x=0.10x$

   so the equation reduces to

   $110091.7431+0.10x=330275.23$

   The net coefficient $0.10$ is the difference of the two rates, $13\%-3\%$: only the rate gap matters, because every unit moved from the low bucket to the high one gains $10\%$.

4. 4

   Isolate the $x$ term.

   $0.10x=330275.23-110091.7431=220183.4869$

5. 5

   Divide by 0.10. Dividing by a tenth means multiplying by ten:

   $x=2201834.869$

6. 6

   Check the answer against the total. The high-rate part contributes $0.13\times 2201834.869=286238.53$ and the low-rate part $0.03\times(3669724.77-2201834.869)=0.03\times 1467889.901=44036.70$. Their sum is $330275.23$ ✓, and $x$ is comfortably below the total $3669724.77$, so the split is meaningful.