with more explanation please

Problem 7. Recall the Making Change problem, where we have an infinite supply of pennies (worth 1 cent), nickels (worth 5 cents), dimes (worth 10 cents), and quarters (worth 25 cents). We take as input an integer n > 0. The goal is to make change for n using the fewest number of coins possible. Prove that in an optimal solution, we use at most 2 dimes