3/5
of the students in a class were boys. The teacher divided the boys equally into groups so that each group of boys had 1 10 of the number of students in the class. The teacher then divided the girls equally into groups such that
each group of girls had
1 5
of the number of students in the class.
a) Find the number of groups of boys and the number of groups of girl
To find the number of groups of boys and the number of groups of girls, we first need to determine the total number of students in the class.
Let's assume the total number of students in the class is represented by "x".
According to the information given, 3/5 of the students in the class were boys. This means there were (3/5)x boys in the class.
The teacher divided the boys equally into groups such that each group of boys had 1/10 of the number of students in the class. This means each group of boys had (1/10)x students.
Therefore, the number of groups of boys can be found by dividing the total number of boys by the number of boys in each group:
Number of groups of boys = (3/5)x / (1/10)x = (3/5) / (1/10) = (3/5) * (10/1) = 3 * 2 = 6
Next, we need to find the number of girls in the class. Since (3/5)x students were boys, then (2/5)x students must be girls.
The teacher divided the girls equally into groups such that each group of girls had 1/5 of the number of students in the class. This means each group of girls had (1/5)x students.
Therefore, the number of groups of girls can be found by dividing the total number of girls by the number of girls in each group:
Number of groups of girls = (2/5)x / (1/5)x = (2/5) / (1/5) = (2/5) * (5/1) = 2 * 1 = 2
So, the number of groups of boys is 6 and the number of groups of girls is 2.
To find the number of groups of boys and girls, we need to determine the total number of students in the class.
Let's assume that there are x students in the class.
Given that 3/5 of the students are boys, we can calculate the number of boys in the class:
Number of boys = (3/5) * x
The teacher divided the boys equally into groups, with each group having 1/10 of the number of students in the class. So the number of boys in each group is:
Number of boys in each group = (1/10) * x
To find the number of groups of boys, we can divide the total number of boys by the number of boys in each group:
Number of groups of boys = (Number of boys) / (Number of boys in each group)
Number of groups of boys = (3/5 * x) / (1/10 * x)
Number of groups of boys = (3/5) / (1/10)
Number of groups of boys = (3/5) * (10/1)
Number of groups of boys = 3 * 10/5
Number of groups of boys = 6
Next, the teacher divided the girls equally into groups, with each group having 1/5 of the number of students in the class. So the number of girls in each group is:
Number of girls in each group = (1/5) * x
To find the number of groups of girls, we can divide the total number of girls by the number of girls in each group:
Number of groups of girls = (Number of girls) / (Number of girls in each group)
Number of groups of girls = ((2/5) * x) / ((1/5) * x)
Number of groups of girls = (2/5) / (1/5)
Number of groups of girls = (2/5) * (5/1)
Number of groups of girls = 2 * 5/5
Number of groups of girls = 2
Therefore, there are 6 groups of boys and 2 groups of girls in the class.
3/5 = 6/10 ... so there were 6 groups of boys
the 2/5 of the class that were girls resulted in 2 groups of 1/5 each
an aside ... the girls' groups were twice as large as the boys' groups