This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
$366
a) To find the number of students in the Yellow Group, we subtract the number of students in the other groups from the total number of students.
Step 1: Find the total number of students in Red, Blue, and Green groups. Step 2: Subtract this sum from the total number of students (40). There were 12 students in the Yellow Group. The student's work for part (a) is ✅ Correct.
b) To find how much the students in the Yellow Group collected, we subtract the amount collected by the other groups from the total amount collected.
Step 1: Find the total amount collected by Red, Blue, and Green groups. Step 2: Subtract this sum from the total amount collected (1040). $$1040 - 674 = 366$$ The students in the Yellow Group collected \boxed{*366*}. The student made a small arithmetic error in their subtraction ( instead of ).
c) To find the average amount collected by each student in the Yellow Group, we divide the total amount collected by the Yellow Group by the number of students in the Yellow Group.
Step 1: Use the amount collected by the Yellow Group from part (b), which is 366. Step 2: Use the number of students in the Yellow Group from part (a), which is 12. Step 3: Divide the amount collected by the number of students. $$\frac{366}{12} = 30.50$$ The average amount collected by each student in the Yellow Group was \boxed{*30.50*}. The student used an incorrect total for the Yellow Group's collection and divided by the total number of students (40) instead of the number of students in the Yellow Group (12).
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a) To find the number of students in the Yellow Group, we subtract the number of students in the other groups from the total number of students.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.