Question

Every 10 years the alumni have a reunion. Every 2 years the alumni have a soccer game. How often do the reunion and the soccer game fall in the same year?

Answer 1

1 times

Explanation:

Hello,

The alumni have reunions every 10 years

But also have football games every 2 years

We have to find how often do the football and reunion fall the same year.

Working with a space of 10 years

In 10 years, reunions happen only once

In 10 years, soccer games happen five times

Assuming we're in the year 2020,

The next reunion would likely occur in year 2030.

But soccer games will happen in year 2022, 2024, 2026, 2028 and finally 2030.

Checking both soccer and reunion coincidence, we can only find one which is in year 2030.

So, soccer games and reunions happen once in 10 years

Answer 2

They would fall in the same year every 10 years

Explanation:

Here in this question, we are interrelated in calculating the number of years it will take the alumni reunion and the alumni soccer game to fall in the same year.

Now looking at the number of years, we can see we have every 2 and every 10 years

To get the year in which they happen at the same time, we can simply find the lowest common multiple of 2 and 10 and that would be 10

This can be visualized in a way that;

The reunion has happened now, and will happen in the next 10 years.

Now since the soccer game has happened now, in the next 10 years, we shall be having 5 episodes. This means that it will take up to the 10th year before we have the soccer game and the alumni reunion occurring at the same time and the mathematical reason for this is that , 10 is the lowest common multiple of 10 and 2