A class of 50 students has to perform exercises in groups of 2 OR 3 students. The numberof groups with 2 students is the same as the number of groups with 3 students.
a) How many groups of 2 students and 3 students can be formed?
b) Each group must use 2 balls to perform its exercise.
What is the total number of balls needed.
a group of 2 and a group of 3 takes 5 students.
Clearly, 10 such pairs of groups can be formed.
a) Well, isn't that a balanced dilemma! If the number of groups with 2 students is the same as the number of groups with 3 students, then we can find the total number of groups by dividing the total number of students (50) by the sum of students in each group (2 + 3 = 5).
So, 50 divided by 5 equals 10. That means there will be a total of 10 groups of 2 students and 10 groups of 3 students.
b) Now let's juggle some math! Since each group needs 2 balls to perform its exercise, we can simply multiply the total number of groups, 20 (10 groups of 2 students + 10 groups of 3 students), by the number of balls per group, 2.
20 groups multiplied by 2 balls per group equals 40 balls.
So, a grand total of 40 balls will be needed to keep the class rolling with their exercises!
To find the number of groups with 2 students and 3 students, we can set up the following equation:
Let x be the number of groups with 2 students.
Then, the number of groups with 3 students is also x.
a) Therefore, we have:
Number of groups with 2 students = Number of groups with 3 students
x = x
The total number of groups is the sum of the number of groups with 2 students and the number of groups with 3 students. So, we have:
Total number of groups = Number of groups with 2 students + Number of groups with 3 students
Total number of groups = x + x = 2x
Since the class has 50 students, the total number of groups will be half of that since each group consists of either 2 or 3 students, so:
2x = 50
Dividing both sides by 2:
x = 25
So, there are 25 groups with 2 students and 25 groups with 3 students.
b) Each group needs 2 balls to perform its exercise. Since we have 25 groups with 2 students and 25 groups with 3 students, the total number of balls needed can be calculated as follows:
Number of balls needed = (Number of groups with 2 students * 2) + (Number of groups with 3 students * 2)
Substituting the given values:
Number of balls needed = (25 * 2) + (25 * 2)
Number of balls needed = 50 + 50
Number of balls needed = 100
Therefore, a total of 100 balls are needed.
To solve this problem, we can break it down into steps.
Step 1: Determine the number of groups of 2 and 3 students.
Let's assume the number of groups with 2 students is x, and the number of groups with 3 students is also x. Since the total number of students is 50, the equation would be:
2x + 3x = 50
Simplifying the equation:
5x = 50
Dividing both sides by 5:
x = 10
Therefore, there are 10 groups of 2 students and 10 groups of 3 students.
a) How many groups of 2 students and 3 students can be formed?
Now that we know there are 10 groups of each type, to find the total number of groups, we can simply add them together:
10 + 10 = 20
So, there are a total of 20 groups that can be formed.
b) Each group must use 2 balls to perform its exercise.
Since each group uses 2 balls, we can calculate the total number of balls needed by multiplying the number of groups by 2:
20 groups x 2 balls/group = 40 balls
Therefore, a total of 40 balls are needed.