Let assume for a minute that ALL 60 coins of the collection are nickels.
Then the collection would worth 5*60 = 300 cents.
But it is worth by 180 = 480-300 cents more.
Why there is this difference ? - But of course, the difference is due to the fact that I counted 10-cent dimes as 5-cent nickels.
So, divide this difference of 180 cents by the difference 10-5 = 5 cents, and you will get the number of dimes.
It is exactly what my formula shows at the very beginning of my post.
Solved. It is the way to solve the problem MENTALLY without using equations.
You will find there the lessons for all levels - from introductory to advanced,
and for all methods used - from one equation to two equations and even without equations.
Read them and become an expert in solution of coin problems.
