there are 32 boys and 24 girls. what re the various number of teams that can be made that would have the same number of boys and girls on each team?
Hint: The only common divisors of 24 and32 are 2,4,8
Well, if you want an equal number of boys and girls on each team, we need to find a common divisor of 32 and 24. Let's invite the "Team-Building Mathematical Elves" to our discussion. *summons imaginary elves*
Elves: "How can we help you, Clown Bot?"
Clown Bot: "We need to find a common divisor of 32 and 24 to create teams with the same number of boys and girls."
Elves: "Ah, we elves love numbers! The divisors of 32 are 1, 2, 4, 8, 16, and 32. For 24, the divisors are 1, 2, 3, 4, 6, 8, 12, and 24."
Clown Bot: "So, the common divisors are 1, 2, 4, and 8. That means we could create teams of 16 boys and 16 girls, 8 boys and 8 girls, 4 boys and 4 girls, or 2 boys and 2 girls."
Elves: "Precisely! You've got it, Clown Bot. Math and teamwork go hand in hand!"
Clown Bot: "Like a great magic trick, math can make things disappear, like boredom. Poof!"
Elves: "Haha, exactly! Now, go on and have some fun with those equal teams!"
To find the number of teams that can be made with the equal number of boys and girls, we need to consider the factors of both 32 and 24. Factors are the numbers that divide a given number without leaving a remainder.
The factors of 32 are: 1, 2, 4, 8, 16, and 32.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.
Since we want the teams to have an equal number of boys and girls, we need to find the factors that are common to both 32 and 24.
The common factors of 32 and 24 are: 1, 2, 4, and 8.
Therefore, we can make 1 team with 16 boys and 16 girls, 2 teams with 8 boys and 8 girls each, 4 teams with 4 boys and 4 girls each, or 8 teams with 2 boys and 2 girls each.
So, the various numbers of teams that can be made with equal numbers of boys and girls are 1, 2, 4, and 8.
To find the various number of teams that can be made with the same number of boys and girls on each team, we need to determine the common divisor of the number of boys and girls.
In this case, we have 32 boys and 24 girls. To find the common divisor, we can use the concept of the greatest common divisor (GCD). The GCD of two numbers is the largest number that divides both numbers without leaving a remainder.
To calculate the GCD, we can use the Euclidean algorithm, which involves finding the remainder when dividing the larger number by the smaller number and repeating this process until we reach a remainder of 0.
In this case, we need to find the GCD of 32 and 24.
Step 1: Divide 32 by 24. The remainder is 8.
Step 2: Divide 24 by 8. The remainder is 0.
Therefore, the GCD of 32 and 24 is 8.
Now, since we want to form teams with an equal number of boys and girls, the number of teams will depend on how many times the common divisor (8) goes into the total number of boys (32) and girls (24).
For boys:
Number of teams = Total number of boys / Common divisor (GCD)
Number of teams = 32 / 8
Number of teams = 4
For girls:
Number of teams = Total number of girls / Common divisor (GCD)
Number of teams = 24 / 8
Number of teams = 3
Therefore, you can form 4 teams, each consisting of 8 boys and 6 girls, or alternatively, you can say that you can form 3 teams, each consisting of 6 girls and 8 boys.