Solve the equation (5399 - x) / x = 4.8116 for x.

Step-by-step solution

1. 1

   Interpret the ratio. The equation states that the part removed from $5399$ is $4.8116$ times as large as $x$ itself. So $5399$ is being split into $x$ plus $4.8116x$, and $x$ should come out roughly one sixth of the total — a useful sanity target before computing.

2. 2

   Multiply through by $x$. Any solution has $x\neq 0$, so

   $5399-x=4.8116x$

3. 3

   Add $x$ to both sides.

   $5399=4.8116x+x=5.8116x$

   The $1$ comes from the $-x$ that was sitting in the numerator; dropping it would give $1122.2$, badly wrong.

4. 4

   Divide.

   $x=\frac{5399}{5.8116}=929.00406\ldots\approx 929.00$

   Rounded to two decimals the trailing digits are $00$, so quoting $929.03$ overshoots by three hundredths.

5. 5

   Check the split. The leftover is $5399-929.00406=4469.99594$, and

   $\frac{4469.99594}{929.00406}=4.81160$

   matching the given ratio to five significant figures, and $929.00+4470.00=5399.00$ recovers the total.