Problem:
A single bench section at a school event can hold either adults or children. When bench sections are connected end to end, an equal number of adults and children seated together will occupy all the bench space. What is the least possible positive integer value of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The least common multiple of and is . Therefore, there must be adults and children.
The total number of benches is
Let denote how many adults there are.
Since the number of adults is equal to the number of children we can write as
Simplifying we get
Since both and have to be positive integers, has to equal . Therefore, is our final answer.
The problems on this page are the property of the MAA's American Mathematics Competitions