Question 8 of 12, Step 1 of 1 Suppose that a university has 23 scholarships to be apportioned among 422 English majors, 335 psychology majors, and 138 graphic design majors. Use the Jefferson method to determine how the scholarships should be apportioned among the three major groups. \[ \begin{array}{l}\text { Answer }\end{array} \]

To apportion the 23 scholarships among the three major groups (English, Psychology, and Graphic Design) using the **Jefferson Method**, follow these steps: ### Step 1: Determine the Initial Divisor The Jefferson Method involves finding a suitable divisor \( d \) such that when each group's population is divided by \( d \) and the result is floored (i.e., rounded down), the total number of apportioned scholarships equals the total available scholarships. ### Step 2: Calculate the Divisor First, estimate the initial divisor \( d \) by dividing the total number of students by the total number of scholarships: \[ d \approx \frac{\text{Total Students}}{\text{Total Scholarships}} = \frac{422 + 335 + 138}{23} \approx \frac{895}{23} \approx 38.913 \] ### Step 3: Adjust the Divisor to Achieve the Total Scholarships We need to find a divisor \( d \) such that: \[ \left\lfloor \frac{422}{d} \right\rfloor + \left\lfloor \frac{335}{d} \right\rfloor + \left\lfloor \frac{138}{d} \right\rfloor = 23 \] Testing with \( d = 36 \): \[ \left\lfloor \frac{422}{36} \right\rfloor = 11 \\ \left\lfloor \frac{335}{36} \right\rfloor = 9 \\ \left\lfloor \frac{138}{36} \right\rfloor = 3 \\ \] \[ 11 + 9 + 3 = 23 \] Thus, \( d = 36 \) satisfies the condition. ### Step 4: Apportion the Scholarships Using \( d = 36 \): - **English Majors**: \( \left\lfloor \frac{422}{36} \right\rfloor = 11 \) scholarships - **Psychology Majors**: \( \left\lfloor \frac{335}{36} \right\rfloor = 9 \) scholarships - **Graphic Design Majors**: \( \left\lfloor \frac{138}{36} \right\rfloor = 3 \) scholarships ### Final Allocation - **English Majors**: **11 scholarships** - **Psychology Majors**: **9 scholarships** - **Graphic Design Majors**: **3 scholarships** This allocation ensures that all 23 scholarships are distributed proportionally based on the number of students in each major using the Jefferson Method. **Answer:** Using the Jefferson method, apportion the 23 scholarships as follows: • English majors – 11 scholarships • Psychology majors – 9 scholarships • Graphic design majors – 3 scholarships