1. **State the problem:** Simplify the expression $$\frac{35x + 37(100 - x)}{100}$$. 2. **Apply the distributive property:** Expand the numerator. $$35x + 37(100 - x) = 35x + 3700 - 37x$$ 3. **Combine like terms:** $$35x - 37x + 3700 = -2x + 3700$$ 4. **Rewrite the expression:** $$\frac{-2x + 3700}{100}$$ 5. **Simplify the fraction by dividing numerator and denominator by 2:** $$\frac{\cancel{2}(-x + 1850)}{\cancel{2}50} = \frac{-x + 1850}{50}$$ 6. **Final simplified expression:** $$\frac{1850 - x}{50}$$ This is the simplified form of the original expression.