12 girls and 20 boys signed up to play n a basketball tournament. Each team needs to have an equal number of girls and boys. What is the greatest number of teams possible
GCD(12,20) = 4
So, 4 teams of 3 girls and 5 boys each
4
I did the work and i'm a teach so it should be right
Well, it seems like the basketball tournament needs to find a way to make sure that the teams have an equal number of girls and boys. Let's see if we can figure this out while keeping things light and fun!
Since we have 12 girls and 20 boys, we need to divide them into teams with equal numbers of both. It's like putting together a delicious sandwich with equal amounts of bread and filling.
Now, let's start by counting the number of teams we can form. We could have 1 team with 6 girls and 6 boys. That's one scrumptious team sandwich!
Or, we could make 2 teams, with each team having 4 girls and 4 boys. That's two perfectly balanced team sandwiches!
Finally, we could form 3 teams, with 3 girls and 3 boys in each team. Three mouthwatering team sandwiches!
So, the greatest number of teams possible in this scenario, while keeping it fair and equal, would be 3.
Now, grab some popcorn and get ready to cheer on those teams as they dribble, shoot, and have a "ball" at the basketball tournament!
To find the greatest number of teams possible, we need to determine the common number of girls and boys that can be evenly divided among the participants.
First, let's find the greatest common divisor (GCD) of the number of girls (12) and boys (20).
To do this, we can use the Euclidean algorithm.
Step 1: Divide the larger number (20) by the smaller number (12).
20 ÷ 12 = 1 remainder 8
Step 2: Divide the previous divisor (12) by the remainder (8).
12 ÷ 8 = 1 remainder 4
Step 3: Divide the previous divisor (8) by the remainder (4).
8 ÷ 4 = 2 remainder 0
Since we have reached a remainder of 0, the GCD is the last remainder, which is 4.
Now let's determine how many teams we can form. We can divide the total number of girls (12) and boys (20) by the GCD (4).
Number of girls per team: 12 ÷ 4 = 3
Number of boys per team: 20 ÷ 4 = 5
Therefore, we can form a maximum of 3 teams, with each team consisting of 3 girls and 5 boys.