Question

2) Mdm Tan takes two classes of students together for music lesson. If she gets them into groups of 6, there will be 19 students left without a group. If she gets them to form the same number of groups, but to get into groups of 8, there will be only 1 student in the last group. If one of the classes has 7 more students than the other, find the class size of the smaller class.​

Answer 1

Answer: 25 students.

Explanation:

Let's assume that the smaller class has x students. Then, the larger class must have x + 7 students.

If Mdm Tan gets the students into groups of 6, there will be 19 students left without a group. This means the total number of students must be 6n + 19 for some integer n:

x + x + 7 = 2x + 7 students (total number of students)

6n + 19 = 2x + 7 (19 students left over)

Solving for x gives x = 25. Therefore, the smaller class has 25 students and the larger class has 32 students.

If Mdm Tan gets the students to form groups of 8, there will be only 1 student in the last group. This means the total number of students must be 8m + 1 for some integer m:

x + x + 7 = 2x + 7 students (total number of students)

8m + 1 = 2x + 7 (1 student left over)

Solving for x using x = 25 gives 8m + 1 = 2(25) + 7 = 57, so m = 7. Therefore, there are 2 groups of 8 with 1 student left over, and the rest of the students form 7 groups of 8.