Columns of two and three

When students in one class stand in columns of two, there is none left. When he stands in columns of three, there is one student left. There are five more double columns than three columns. How many students are in the class?

Final Answer:

n =  28

Step-by-step explanation:


n=2x
n = 3y+1
x=5+y

n=2·x
n = 3·y+1
x=5+y

n-2x = 0
n-3y = 1
x-y = 5

Row 2 - Row 1 → Row 2
n-2x = 0
2x-3y = 1
x-y = 5

Row 3 - 1/2 · Row 2 → Row 3
n-2x = 0
2x-3y = 1
0.5y = 4.5


y = 4.5/0.5 = 9
x = 1+3y/2 = 1+3 · 9/2 = 14
n = 0+2x = 0+2 · 14 = 28

n = 28
x = 14
y = 9

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