The coin box of a vending machine contains $6.20 in dimes and quarters. There are 32 coins in all. How many of each kind are there?

Let d and q be the number of dimes and quarters respectively.

10 cents * d + 25 cents * q = 620 cents ($6.20 = 620 cents)

⇒ 10d + 25q = 620 (1)

On the other hand, we have: d + q = 32 (coins) (2)

From (1) and (2), we solve the set of equations.

The final answer is d = 12 coins and q = 20 coins.