Question 1132092
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(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.<br>
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....<br>
(b) 1/2 + 1/3 + 1/9 = 17/18.<br>
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.<br>
Since exactly 1 boy was borrowed; there is only one answer to this problem: your class has 17 students.