Questions: In order for a student to win a position with the Student Government Association at Williams Central High School, they must secure at least 35% of the votes from each class. There are a total of 1200 students in the high school and the ratio of freshmen to sophomores to juniors to seniors is 3: 4: 5: 4, respectively. Minimally, how many votes from the junior class must one earn for consideration?

Solution Steps

The total number of students is 1200, and the ratio of freshman:sophomores:juniors:seniors is \(3:4:5:4\). To find the number of students in each class, we first calculate the total number of parts in the ratio: \[ 3 + 4 + 5 + 4 = 16 \text{ parts}. \] Next, we determine the number of students per part: \[ \text{Students per part} = \frac{1200}{16} = 75. \] Now, we calculate the number of students in each class:

• Freshman: \(3 \times 75 = 225\),
• Sophomores: \(4 \times 75 = 300\),
• Juniors: \(5 \times 75 = 375\),
• Seniors: \(4 \times 75 = 300\).

To secure at least \(35\%\) of the votes from the junior class, we calculate: \[ \text{Minimum votes} = 0.35 \times 375 = 131.25. \] Since the number of votes must be a whole number, we round up to the nearest whole number: \[ \text{Minimum votes} = 132. \]

Final Answer