The senior class was being lined up by height-shortest to tallest- for the graduation ceremony. Bert is shorter than Phillip, Jessie is taller than Michelle,and Michelle is shorter than Bert. Once they were lined up, Phillip was three people taller than Michelle, and Michelle was two people away from Jessie. How were these students arranged for graduation?
Thanks
Michelle then Bert then Jessie then Phillip. Michelle and Phillip are three people apart, and Phillip is the tallest. Jessie is two away from Michelle. That leaves Bert second shortest.
To solve this problem, we can use deductive reasoning and create a step-by-step approach.
1. Start with the given information:
- Bert is shorter than Phillip
- Jessie is taller than Michelle
- Michelle is shorter than Bert
2. Let's denote the students as follows:
- Bert = B
- Phillip = P
- Jessie = J
- Michelle = M
3. Use the given information to create a few initial deductions:
- B < P
- J > M
- M < B
4. Next, consider the statement "Phillip was three people taller than Michelle."
- This means that the number of people between P and M is 3. We can represent this as:
P - - - M
5. From the given statement "Michelle was two people away from Jessie," we can make two deductions:
- M is either 2 positions away from J or J is 2 positions away from M.
- Since we already know J > M, M cannot be two positions away from J because it would place J below M. Therefore, we conclude:
M - - J
6. Combining the deductions from steps 4 and 5, we can represent two possible arrangements:
a) M - - J, and P - - - B
b) J - - M, and P - - - B
7. Consider the statement "The senior class was being lined up by height-shortest to tallest." This means we need to arrange the students in ascending order by height.
8. Option (a) M - - J, and P - - - B:
- Since the order from shortest to tallest is B, M, J, and P, this option does not fulfill the requirement.
9. Option (b) J - - M, and P - - - B:
- Since the order from shortest to tallest is B, P, M, and J, this option fulfills the requirement.
- Therefore, the correct arrangement is: Bert, Phillip, Michelle, Jessie.
So, the students were arranged as follows at the graduation ceremony: Bert, Phillip, Michelle, Jessie.