1. **State the problem:** We are given a total of 175 teachers to be apportioned among five high schools based on their student populations using Webster's method. 2. **List the populations:** Owen = 875, East = 1150, Lincoln = 1200, Laurel = 725, Dale = 925, Total students = 4875. 3. **Webster's method** involves finding a divisor such that when each school's population is divided by it and the results rounded to the nearest integer, the total assigned teachers is 175. 4. **Step 1:** Calculate an initial divisor by dividing total students by total teachers: $$\text{divisor} = \frac{4875}{175} = 27.8571.$$ 5. **Step 2:** Divide each school's population by the divisor and round to the nearest integer: - Owen: $\frac{875}{27.8571} \approx 31.41 \to 31$ - East: $\frac{1150}{27.8571} \approx 41.30 \to 41$ - Lincoln: $\frac{1200}{27.8571} \approx 43.06 \to 43$ - Laurel: $\frac{725}{27.8571} \approx 26.03 \to 26$ - Dale: $\frac{925}{27.8571} \approx 33.21 \to 33$ Sum: $31 + 41 + 43 + 26 + 33 = 174$ teachers, which is 1 less than 175. 6. **Step 3:** Adjust the divisor slightly to increase total teachers assigned to 175. Try divisor = 27.7: - Owen: $\frac{875}{27.7} \approx 31.58 \to 32$ - East: $\frac{1150}{27.7} \approx 41.52 \to 42$ - Lincoln: $\frac{1200}{27.7} \approx 43.32 \to 43$ - Laurel: $\frac{725}{27.7} \approx 26.17 \to 26$ - Dale: $\frac{925}{27.7} \approx 33.40 \to 33$ Sum: $32 + 42 + 43 + 26 + 33 = 176$ teachers, which is 1 more than 175. 7. **Step 4:** Try averaging divisor to 27.78: - Owen: $\frac{875}{27.78} \approx 31.50 \to 32$ - East: $\frac{1150}{27.78} \approx 41.41 \to 41$ - Lincoln: $\frac{1200}{27.78} \approx 43.20 \to 43$ - Laurel: $\frac{725}{27.78} \approx 26.10 \to 26$ - Dale: $\frac{925}{27.78} \approx 33.29 \to 33$ Sum: $32 + 41 + 43 + 26 + 33 = 175$ teachers total. **Final assignments:** Owen = 32, East = 41, Lincoln = 43, Laurel = 26, Dale = 33.