Journey to school

On the way to school, I took a steady step. In the first half of the journey, I counted every second step, and in the second half, every third. How many steps did I take when I went to school? If I counted, double steps are 250 more than three steps?

Correct answer:

n =  3000

Step-by-step explanation:


a = 250 + b
x = 2a + 3b
2a = 3b

a = 250 + b
x = 2·a + 3·b
2·a = 3·b

a-b = 250
2a+3b-x = 0
2a-3b = 0

Pivot: Row 1 ↔ Row 2
2a+3b-x = 0
a-b = 250
2a-3b = 0

Row 2 - 1/2 · Row 1 → Row 2
2a+3b-x = 0
-2.5b+0.5x = 250
2a-3b = 0

Row 3 - Row 1 → Row 3
2a+3b-x = 0
-2.5b+0.5x = 250
-6b+x = 0

Pivot: Row 2 ↔ Row 3
2a+3b-x = 0
-6b+x = 0
-2.5b+0.5x = 250

Row 3 - -2.5/-6 · Row 2 → Row 3
2a+3b-x = 0
-6b+x = 0
0.083x = 250


x = 250/0.08333333 = 3000
b = 0-x/-6 = 0-3000/-6 = 500
a = 0-3b+x/2 = 0-3 · 500+3000/2 = 750

a = 750
b = 500
x = 3000

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