Solve the equation (16939 - x) / x = 0.923 for x.

Step-by-step solution

1. 1

   Note what the equation is saying. The numerator $16939-x$ is what is left of the total $16939$ after removing $x$, so the equation says the leftover is $0.923$ times $x$. That reading predicts the shape of the answer: total $=x+0.923x$, hence $x=$ total$/1.923$.

2. 2

   Clear the denominator. Since a solution must have $x\neq 0$ (otherwise the left side is undefined), multiply both sides by $x$:

   $16939-x=0.923x$

3. 3

   Collect the $x$ terms — this is where the '+1' lives. Add $x$ to both sides:

   $16939=0.923x+x=1.923x$

   The coefficient is $1.923$, not $0.923$: forgetting to include the $x$ that came from the numerator is the standard error here.

4. 4

   Divide to isolate $x$.

   $x=\frac{16939}{1.923}=8808.6323\ldots\approx 8808.63$

   Exactly, $x=\dfrac{16939000}{1923}$, which does not reduce ($1923=3\cdot 641$ and $16939000$ is not a multiple of $3$).

5. 5

   Substitute back to check the fourth decimal. With $x=8808.6323$ the leftover is $16939-8808.6323=8130.3677$, and

   $\frac{8130.3677}{8808.6323}=0.92300$

   as required. The commonly quoted $8809.67$ gives $0.92277$ instead, which is why it is not the solution.