# A potter makes pots and arranges them in rows for drying. How many pots does the potter make?

A potter makes more than $$100$$ but less than $$300$$ pots and arranges them in rows, with each row consisting of the same number of pots, for drying. He finds that if he places $$6$$ pots more per row, he can arrange the pots in $$10$$ less rows. How many pots does the potter make?

The answer to this question is given as $$225$$ but I obtained $$120$$ also as one of the possible solutions.

Is $$120$$ wrong? If yes, why?

Here's how I obtained the solutions:

Let the number of rows be $$n$$ and the number of pots per row be $$x$$ the we have $$nx=(n-10)(x+6)$$ Which is same as $$3n-5x=30$$ Solving it as a Diophantine equation, we obtain solutions for $$(n,x)$$ as $$(10,0), (15,3), (20,6), (25,9), (30,12), \dots$$

Since $$100 so, we have solutions as $$(20,6)$$ and $$(25,9)$$.

• You ought to explain your work, but I agree that $(120,20)$ is a valid solution, as is $(225,25)$.
– lulu
Jun 8, 2022 at 11:04
• @MathLover I'm editing my question, my apologies Jun 8, 2022 at 11:35
• Yes your work is correct. +1 Jun 8, 2022 at 11:46

Yes, the working is correct and $$(120,20)$$ is a valid solution, as is $$(225,25)$$.