Solve for x: x = 0.35 * 200 + 0.35x.

Step-by-step solution

1. 1

   Evaluate the numeric product first. $0.35\times200=70$, so the equation reduces to

   $x=70+0.35x$

   Now the only difficulty is that $x$ appears on both sides.

2. 2

   Recognise why you cannot just divide. A common wrong move is to read this as $x=70/0.35=200$. That ignores the $x$ on the right. Because $x$ is defined partly in terms of itself, the $x$ terms must be gathered before any division.

3. 3

   Move the 0.35x to the left. Subtract $0.35x$ from both sides:

   $x-0.35x=70\qquad\Longrightarrow\qquad (1-0.35)x=70\qquad\Longrightarrow\qquad 0.65x=70$

   The coefficient $1-0.35=0.65$ is what the self-reference costs you.

4. 4

   Divide by 0.65.

   $x=\frac{70}{0.65}=\frac{7000}{65}=\frac{1400}{13}=107.6923\ldots\approx107.69$

   Writing it as the exact fraction $\tfrac{1400}{13}$ makes clear the decimal never terminates.

5. 5

   Verify by substituting back. With $x=\tfrac{1400}{13}$: the right side is $70+0.35\cdot\tfrac{1400}{13}=70+\tfrac{490}{13}=\tfrac{910+490}{13}=\tfrac{1400}{13}$, which equals the left side exactly ✓. Note the answer $107.69$ is larger than $70$ but much smaller than the naive $200$ — a good reminder of why the collection step matters.