Ron has 14 coins with a total value of $2.50. The coins are nickels and quarters. How many of each coin does he have?

Let n be the number of nickels.
Then, the number of quarters = 14 - n

Total amount :
0.05n + 0.25(14 - n) = 2.50
0.05n + 3.5 - 0.25n = 2.5
0.2n = 1
n = 5
14 - n = 9

The number of nickels = 5
The number of quarters = 9

14 nickels would be $0.70. Replacing one nickel with a quarter adds $0.20 to the total.

You need to replace enough nickels to add $2.50 - $0.70 to the total, for $1.80 increase. That takes 1.80 / 0.20 = 9 quarters, replacing 9 of the nickels,

The remaining 5 nickels were not replaced, so you have 9 quarters and 5 nickels. As a check, 5 nickels make one quarter, and 10 quarters obviously add up to $2.50.

This sort of "number sense" approach works with a lot of problems.

-5 nickels and 9 quarters