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

Step-by-step solution

1. 1

   Simplify the denominator. $1-0.0152 = 0.9848$, so the equation reads $295 = x + 0.0152\cdot\frac{0.0152x}{0.9848}.$

2. 2

   Multiply the two percentage factors. Both $0.0152$ factors multiply together: $0.0152 \times 0.0152 = 0.00023104.$ This is the crucial observation - a $1.52\%$ rate applied twice is not $3.04\%$ but roughly $0.023\%$.

3. 3

   Form the single coefficient of x. $\frac{0.00023104}{0.9848} = 0.000234606\ldots$ so the equation collapses to $295 = x + 0.000234606\,x.$

4. 4

   Factor out x and divide. $295 = x\,(1+0.000234606) = 1.000234606\,x \Longrightarrow x = \frac{295}{1.000234606} \approx 294.9308.$

5. 5

   Verify by substitution. $294.9308 + 0.0152\cdot\dfrac{0.0152\times294.9308}{0.9848} = 294.9308+0.0692 = 295.0000$, so the root is correct.

6. 6

   Reject the commonly quoted value 111.241. Substituting $x=111.241$ gives $111.241+0.0261 = 111.267 \neq 295$, so that number does not solve this equation - it presumably belongs to a differently structured formula. Because the added term is only about $0.023\%$ of $x$, any correct answer must sit just below $295$.