Solve for x: 295 = x + 0.0152 + (x times 0.0152)/(1 - 0.0152).

Step-by-step solution

1. 1

   Move the lone constant across. Only $0.0152$ on its own is free of $x$:

   $295-0.0152=x+\frac{0.0152x}{0.9848}\ \Longrightarrow\ 294.9848=x+\frac{0.0152x}{0.9848}.$

   Note that $0.0152$ appears twice in the problem with two different roles — once as a flat amount and once as a rate. Keeping them apart is the main hazard here.

2. 2

   Factor x out of the right-hand side.

   $294.9848=x\left(1+\frac{0.0152}{0.9848}\right).$

3. 3

   Compute the gross-up multiplier.

   $\frac{0.0152}{0.9848}=0.01543461\ldots\ \Longrightarrow\ 1+0.01543461=1.01543461.$

4. 4

   Divide.

   $x=\frac{294.9848}{1.01543461}=290.50103.$

5. 5

   Substitute back to confirm. The fee term is $\dfrac{0.0152\times 290.50103}{0.9848}=4.48347$, so the right side is

   $290.50103+0.0152+4.48347=295.00000,$

   reproducing the left side. So $x\approx 290.50$.