Question

or An equal number of elementary school students and secondary school students in Sullivan get to school by bus. The bus that carries elementary school students transports groups of 14 at a time, while the bus that carries secondary school students transports groups of 16 at a time. What is the minimum number of each type of student that the county must have?

Answer 1

Let's assume the number of elementary school students is "E" and the number of secondary school students is "S".

According to the information given:

1. The number of elementary school students must be a multiple of 14, since they travel in groups of 14.

2. The number of secondary school students must be a multiple of 16, since they travel in groups of 16.

To find the minimum number of each type of student, we need to find the least common multiple (LCM) of 14 and 16.

LCM(14, 16) = 112

So, the minimum number of elementary school students (E) and secondary school students (S) that the county must have are both 112.

This means the county must have 112 elementary school students and 112 secondary school students in order to ensure that the buses can transport them in the specified group sizes.