Journey to school

On the way to school, I walked at a steady pace. In the first half of the journey, I counted every second step, and in the second half, every third step. How many steps did I take to get to school, if the count of double-steps was 250 more than the count of triple-steps?

Final Answer:

n =  3000

Step-by-step explanation:

$$\begin{gathered} 2a=3b \\ a=250+b \\ 3b/2=250+b \\ 3\cdot b/2=250+b \\ b=500 \\ a=250+b=250+500=750 \\ n=2\cdot a+3\cdot b=2\cdot 750+3\cdot 500=3000 \end{gathered}$$

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