Suppose tom has 16 coins totaling $2.50. if he has only dimes and quarters, how many of each type does he have?

Suppose that Tom has x quarters. Since Tom has 16 coins in all, the rest of the coins, 16 - x of them, must be nickels.

The value of x dimes is 0.25x dollars (since each quarter is 25 cents), and the value of 16 - x dimes is 0.10(16 - x) (since each dime is 10 cents). The total value of these coins, in dollars, is:
0.25x + 0.10(16 - x).

Since these coins are worth $2.50, we have the equation:
0.25x + 0.10(16 - x) = 2.50.

Solving this yields x = 6. Therefore, Tom has 6 quarters and 16-6 = 10 dimes.