Solve the equation (9127 - x) / x = 0.934 for x.

Step-by-step solution

1. 1

   Read what the ratio means. The numerator is the part of $9127$ left after removing $x$, so the equation says the leftover is $0.934$ times $x$. Since $0.934$ is just under $1$, the two parts are nearly equal and $x$ should come out slightly above half of $9127$, i.e. a little over $4563$.

2. 2

   Clear the denominator. A solution must have $x\neq 0$, so multiplying by $x$ is safe:

   $9127-x=0.934x$

3. 3

   Collect the $x$ terms. Adding $x$ to both sides:

   $9127=0.934x+x=1.934x$

   The coefficient is $1.934$, not $0.934$ — the extra $1$ comes from the $-x$ that was in the numerator.

4. 4

   Divide.

   $x=\frac{9127}{1.934}=4719.2347\ldots\approx 4719.23$

   Exactly, $x=\frac{9127000}{1934}=\frac{4563500}{967}$, which does not reduce further ($967$ is prime).

5. 5

   Substitute back to four decimals. The leftover is $9127-4719.2347=4407.7653$, and

   $\frac{4407.7653}{4719.2347}=0.93400$

   exactly as required. By contrast $4719.75$ gives $0.93379$, which misses the target ratio, so it is not the solution.