Question

a marching band is having difficulty in getting line up. when lined up in 3, 2 people are left out and when line up in 4, 3 people are left out. What is the number of people?​

Answer 1

The least number of people in a marching band that satisfies the given conditions is found to be 11.

Step-by-step explanation:

The problem presented involves finding the smallest number of people in a marching band that can’t line up evenly in groups of 3 or 4, with respectively 2 and 3 left over. This is a problem that can be solved using number theory and the concept of least common multiple (LCM).

Step-by-step explanation:

Let the number of people in the band be n. We can express the problem mathematically as the following two equations:

n mod 3 = 2, which means when n is divided by 3, the remainder is 2.

n mod 4 = 3, which means when n is divided by 4, the remainder is 3.

To solve this, start with the knowledge that n = 3k + 2 for some integer k.

Check multiples of 3 plus 2 (5, 8, 11, 14, ...) until you find one that also satisfies n mod 4 = 3.

Through trial and error, n = 11 is the first number to satisfy both conditions. Therefore, the band has 11 members.