In a tennis club, the lockers are placed side by side and are numbered from 1 to 40.
A membership of greater than three years means the locker is tagged with a red tag. A member who is a pro has his locker tagged with a green tag. It was found that every third locker is marked with a red tag and every fourth locker is marked with a green tag. Some lockers have both tags.
Which locker will be the first to represent a member who has been with the club more than three years and is a pro?
To find the locker that will be the first to represent a member who has been with the club more than three years and is a pro, we can use the concept of finding the least common multiple (LCM) of two numbers.
Let's start by finding the locker numbers that are marked with red tags, green tags, or both tags.
The lockers marked with red tags are those numbered with multiples of 3: 3, 6, 9, 12, ... up to 39.
The lockers marked with green tags are those numbered with multiples of 4: 4, 8, 12, 16, ... up to 40.
Now, we need to find the smallest locker number that appears in both of these sets. This will represent the locker that has both red and green tags.
To find the smallest locker number that appears in both sets, we need to find the least common multiple (LCM) of 3 and 4.
The LCM of two numbers is the smallest multiple that is divisible by both numbers.
The prime factorization of 3 is 3 (3 = 3^1).
The prime factorization of 4 is 2^2.
To find the LCM, we need to take the highest power of each prime factor that appears in either number. That gives us: 2^2 * 3^1 = 12.
Therefore, the least common multiple (LCM) of 3 and 4 is 12.
So, the locker number 12 is the first locker to represent a member who has been with the club more than three years and is a pro (having both red and green tags).
Hence, locker number 12 will be the answer.