SOLUTION: a)My maths teacher is dividing my class into groups. She makes two groups, each with a quarter of the class and three groups each with one-sixth of the class. How many are there in

Question 1132092: a)My maths teacher is dividing my class into groups. She makes two groups, each with a quarter of the class and three groups each with one-sixth of the class. How many are there in the class?
b) My English teacher wants to divide our class into one half, one third and one ninth but the division will not go exactly. He borrows a boy from the class next door, does the division (which works out exactly, with a whole number of us in each group) and then sends him back. How many are there in the class?
Regards
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(a) 2(1/4)+3(1/6) = 1, so all the students are in groups. The number of students can be any number for which 1/4 of the students and 1/3 of the students are whole numbers.

Since the least common multiple of 3 and 4 is 12, the number of students can be any multiple of 12.
12 students = 2 groups of 3 and 3 groups of 2
24 students = 2 groups of 6 and 3 groups of 4
36 students = 2 groups of 9 and 3 groups of 6
etc., etc....

(b) 1/2 + 1/3 + 1/9 = 17/18.

So the teacher borrows one boy from the other class to make 18. Then 1/2 of 18 = 9; 1/3 of 18 = 6; and 1/9 of 18 = 2; 9+6+2 = 17. Then the borrowed boy is sent back to his class.

Since exactly 1 boy was borrowed; there is only one answer to this problem: your class has 17 students.
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