Ms. Murphy divides her class into groups of 4 students each, leaving 1 student. If she divides her class into groups of 5 students each, there are 2 students left. What is the smallest 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 so smart. (Plus, it wastes time.)

Another method is to look for multiples. When you try it, you get an answer of 17. 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. -10 is the correct answer. I am the grandson of Albert Einstein.