Solve x times 75 times 365 divided by 1000 equals 137.1 for x.

Step-by-step solution

1. 1

   Collapse the chain of constants into one coefficient. Everything except $x$ is numeric, so multiply it out once:

   $75\cdot 365=27375,\qquad \frac{27375}{1000}=27.375$

   The equation is therefore the simple linear equation $27.375x=137.1$. (The shape $\text{rate}\times 75\times 365/1000$ is typical of an annual total built from a daily figure, with the $1000$ converting units.)

2. 2

   Divide to isolate $x$.

   $x=\frac{137.1}{27.375}$

3. 3

   Convert to an exact fraction. Scale both parts by $1000$ and cancel:

   $\frac{137.1}{27.375}=\frac{137100}{27375}=\frac{75\cdot 1828}{75\cdot 365}=\frac{1828}{365}$

   So the exact answer is $\frac{1828}{365}$, which does not reduce to $5$ ($5$ would need the numerator to be $1825$).

4. 4

   Write the decimal. $365\cdot 5=1825$ with remainder $3$, so

   $x=5+\frac{3}{365}=5.008219\ldots\approx 5.0082$

5. 5

   Test the tempting round answer. Substituting $x=5$ gives

   $\frac{5\cdot 75\cdot 365}{1000}=\frac{136875}{1000}=136.875$

   which falls $0.225$ short of $137.1$, so $x=5$ is not a solution. Substituting $x=1828/365$ instead gives $\frac{1828\cdot 75}{1000}=\frac{137100}{1000}=137.1$ exactly.