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Joseph instructed her fifteen students to stand in a straight line at a distance of 1 meter each and assigned numbers 1 to 15 to each student in such a way that odd numbers were given to boys and even numbers were given to girls.

1. Find the number of girls and number of boys who participated in the game.
2. What is the distance between the third and twelfth student?
3. Mrs. Joseph told the students to make groups of two students in such a way that their assigned number sums to 12.

Sagot :

GinnyAnsweridn
Let's solve each part of the question step by step.

### 1. Determine the number of boys and girls:

1. Number of Boys:
- Boys were assigned odd numbers.
- The total number of students is 15, and they are numbered from 1 to 15.
- Odd numbers within this range are: 1, 3, 5, 7, 9, 11, 13, 15.
- Therefore, there are 8 boys.

2. Number of Girls:
- Girls were assigned even numbers.
- Even numbers within this range are: 2, 4, 6, 8, 10, 12, 14.
- Therefore, there are 7 girls.

Summary:
- Number of Boys: 8
- Number of Girls: 7

### 2. Distance between the third and twelfth student:

- Each student stands 1 meter apart.
- The position numbers of the third and twelfth students are 3 and 12, respectively.
- To find the number of students between them, subtract the position of the third student from the position of the twelfth student: [tex]\( 12 - 3 \)[/tex].
- This gives us [tex]\( 9 \)[/tex] students between the third and twelfth students.

Distance:
- The distance is [tex]\( 9 \)[/tex] meters.

### 3. Pairs of students whose assigned numbers add up to 12:

- We need to find pairs of numbers between 1 and 15 that add up to 12.
- Let's list down all possible pairs:
- (1, 11)
- (2, 10)
- (3, 9)
- (4, 8)
- (5, 7)
- (6, 6) would not be a pair as it requires the same student to be counted twice.

Valid Pairs:
- (1, 11)
- (2, 10)
- (3, 9)
- (4, 8)
- (5, 7)

### Final Step-By-Step Solution Summary:

1. Number of Boys: 8
2. Number of Girls: 7
3. Distance between the third and twelfth students: 9 meters
4. Pairs of students whose assigned numbers add up to 12: [tex]\( (1, 11), (2, 10), (3, 9), (4, 8), (5, 7) \)[/tex]

Hence, we have successfully addressed all parts of the problem systematically.
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