Solve for x: 1600W times 8% + 1600W times 2% + 3200W times 0.0006 + 0.13x + 3200W times 1% = x.

Step-by-step solution

1. 1

   Convert the percentages and note what kind of equation this is. Replacing $8\%=0.08$, $2\%=0.02$, $1\%=0.01$ leaves $x$ on both sides. That makes it a linear equation to be solved, not an expression to be evaluated - the $0.13x$ term cannot simply be added up with the constants.

2. 2

   Evaluate each constant term separately.

   $1600W(0.08)=128W,\quad 1600W(0.02)=32W$

   $3200W(0.0006)=1.92W,\quad 3200W(0.01)=32W$

3. 3

   Add the constant terms.

   $128W+32W+1.92W+32W=193.92W$

   so the equation reads $193.92W+0.13x=x$.

4. 4

   Collect the $x$ terms on one side. Subtracting $0.13x$ from both sides:

   $193.92W=x-0.13x=0.87x$

   The coefficient $0.87=1-0.13$ is the point of the whole problem: only $87\%$ of $x$ is left over to balance the fixed losses.

5. 5

   Divide by $0.87$.

   $x=\frac{193.92W}{0.87}=222.8966W$

6. 6

   Substitute back to check. With $x=222.8966W$, the left side is $193.92W+0.13(222.8966W)=193.92W+28.9766W=222.8966W$, which equals the right side ✓.