Answer :
Answer:
x = 119
Step-by-step explanation:
Solution:-
- The number of students in a marching band = x
- When they Line up in "twos" there is 1 left over, That if we mathematically express it:
Division: x / 2 , Remainder = 1
- When they Line up in "threes" there is 2 left over, That if we mathematically express it:
Division: x / 3 , Remainder = 2
- When they Line up in "fours" there is 3 left over, That if we mathematically express it:
Division: x / 4 , Remainder = 3
When they Line up in "fives" there is 4 left over, That if we mathematically express it:
Division: x / 5 , Remainder = 4
When they Line up in "sixes" there is 5 left over, That if we mathematically express it:
Division: x / 6 , Remainder = 5
When they Line up in "sevens" there are no left over, That if we mathematically express it:
Division: x / 7 , Remainder = 0
- It means that the total number of "x" students are perfectly divisible by 7. If it is not divisible by 2, then it is an odd number.
- So,
x = 7 * a
Where, x > 7 and exclude derivative multiples of (5, 4 , 6)
- So from trial and error, a = 17
x = 119
Using multiples and remainder of divisions, it is found that there were 119 students there.
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- When they line up in sevens, no students remain, thus, the number of students is a multiple of 7.
- When they line up in two's, there is 1 left over, thus, the number of students is odd.
- When they line up in three's, there are 2 left over, thus, the remainder of the division of the number of students n and 3 is 2.
- When they line up in fives, there are 4 left over, thus, the remainder of the division of the number of students n and 5 is 4.
- When they line up in sixes there are 5 left over, thus, the remainder of the division of the number of students n and 6 is 5.
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Shortening the possibilities, we look at odd multiples of 7, which are: {7, 21, 35, 49, 63, 77, 91, 105, 119, ...}
- 21, 63 and 105 are multiples of 3, so these are not the number of students.
- 35 is multiple of 5, so it is also disconsidered.
- The remainder of the division of 119 and 3 is 2.
- The remainder of the division of 119 and 5 is 4.
- The remainder of the division of 119 and 6 is 5.
Thus, 119 is the number of students.
A similar problem is given at https://brainly.com/question/21644206