Let

'x' be the number of nickles. Since one nickle is 5 cents this means that i have 5*x cents.

'y' be the number of quarters. Since one quarter is 25 cents this means that i have 25*y cents.

Then we can write down the following

x + y = 30 (the total number of nickles and quarters)

5*x + 25*y = 4.10*100 ($1 = 100 cents)

The solution of the system

x + y = 30

5*x + 25*y = 410

will give the answer

x = 17 nickles

y = 13 quarters

Indeed 17 + 13 = 30 and 5*17 + 25*13 = 410

I have 17 nickles and 13 quarters.