1. **State the problem:** Solve for $B$ in the equation $$\frac{B + 0.12(100 - B)}{0.58} = 28.57.$$\n\n2. **Write the formula and explain:** We want to isolate $B$. The equation involves a fraction, so we will first eliminate the denominator by multiplying both sides by $0.58$.\n\n3. **Multiply both sides by $0.58$: $$B + 0.12(100 - B) = 28.57 \times 0.58.$$**\nCalculate the right side: $$28.57 \times 0.58 = 16.5706.$$\nSo, $$B + 0.12(100 - B) = 16.5706.$$\n\n4. **Distribute $0.12$ inside the parentheses:** $$B + 0.12 \times 100 - 0.12B = 16.5706.$$\nSimplify: $$B + 12 - 0.12B = 16.5706.$$\n\n5. **Combine like terms:** $$B - 0.12B = 0.88B,$$ so the equation becomes $$0.88B + 12 = 16.5706.$$\n\n6. **Subtract 12 from both sides:** $$0.88B + 12 - 12 = 16.5706 - 12,$$ which simplifies to $$0.88B = 4.5706.$$\n\n7. **Divide both sides by 0.88:** $$B = \frac{4.5706}{0.88}.$$\nShow cancellation: $$B = \frac{\cancel{4.5706}}{\cancel{0.88}}$$ (just indicating division).\nCalculate the division: $$B \approx 5.193.$$\n\n**Final answer:** $$\boxed{B \approx 5.19}.$$