1. Stating the problem: Calculate the value of $x_b$ given by the formula $$x_b = \frac{700}{700+300} \times (600-70)$$ 2. Formula and explanation: This formula calculates a weighted portion of the difference between 600 and 70, where the weight is the fraction $\frac{700}{700+300}$. 3. Calculate the denominator: $$700 + 300 = 1000$$ 4. Substitute back into the fraction: $$x_b = \frac{700}{1000} \times (600 - 70)$$ 5. Simplify the fraction by canceling common factors: $$x_b = \frac{\cancel{700}}{\cancel{1000}} \times (600 - 70) = \frac{7}{10} \times (600 - 70)$$ 6. Calculate the difference inside the parentheses: $$600 - 70 = 530$$ 7. Multiply the fraction by the difference: $$x_b = \frac{7}{10} \times 530 = 7 \times 53 = 371$$ Final answer: $$x_b = 371$$