Sophia is selecting a planning committee for her schools annual talent show. The committee must consist of 12 students with members from both the freshmen and sophomore classes. At least two students must be from each class. Which of the following is a viable solution for this situation.

Question

A. 1 freshman and 11 sophomores
B. 0 freshmen and 12 sophomores
C. 6 freshman and 4 sophomore
D. 5 freshmen and 7 sophomores

Answer 1

To determine which option is viable for Sophia's planning committee, we need to ensure that the committee has at least 2 members from both freshmen and sophomore classes while totaling 12 members.

Let's analyze each option:

A. 1 freshman and 11 sophomores

• Freshmen: 1 (less than 2, so not a viable option)
• Sophomores: 11
• Not viable.

B. 0 freshmen and 12 sophomores

• Freshmen: 0 (less than 2, so not a viable option)
• Sophomores: 12
• Not viable.

C. 6 freshmen and 4 sophomores

• Freshmen: 6 (at least 2, so this is viable)
• Sophomores: 4 (at least 2, so this is viable)
• Total: 6 + 4 = 10 (Should total 12, so this is not viable)
• Not viable.

D. 5 freshmen and 7 sophomores

• Freshmen: 5 (at least 2, so this is viable)
• Sophomores: 7 (at least 2, so this is viable)
• Total: 5 + 7 = 12 (meets the total requirement)
• Viable solution.

Based on the analysis, the only viable solution is:

D. 5 freshmen and 7 sophomores.