Mrs. Murphy separates her class into groups of 4 students each, 1 student is left over. If she separates her class into groups of 5 students each, 2 students are left over. What is the least number of students the class could have?
4k+1 = 5n+2
4k = 5n+1
So, what multiple of 4 is 1 more than a multiple of 5?
k=4, n=3
So, 17 students.
17
17
17
One way is to draw a diagram. But that makes you look not that smart. (Besides, it wastes time.)
Another way is to look for multiples. When you try it, you get 17 as an answer.
17
17
4k+1 = 5n+2
4k = 5n+1
So, what multiple of 4 is 1 more than a multiple of 5?
k=4, n=3
So, 17 students.