1. **State the problem:** Solve the equation $0.88 = \frac{558 + x}{700 + x}$ for $x$. 2. **Use the formula:** To solve for $x$, multiply both sides by the denominator to eliminate the fraction: $$0.88(700 + x) = 558 + x$$ 3. **Distribute and simplify:** $$0.88 \times 700 + 0.88x = 558 + x$$ $$616 + 0.88x = 558 + x$$ 4. **Isolate $x$ terms:** Subtract $0.88x$ from both sides: $$616 + \cancel{0.88x} - \cancel{0.88x} = 558 + x - 0.88x$$ $$616 = 558 + 0.12x$$ 5. **Isolate $x$:** Subtract 558 from both sides: $$616 - 558 = 0.12x$$ $$58 = 0.12x$$ 6. **Solve for $x$:** Divide both sides by 0.12: $$\frac{58}{\cancel{0.12}} = \frac{0.12x}{\cancel{0.12}}$$ $$x = \frac{58}{0.12}$$ 7. **Calculate the value:** $$x = 483.33$$ **Final answer:** $x = 483.33$