There are a total of 15 dimes and quarters in a covered cup. The value of all 15 coins totals 2.85

There are 6 dimes and 9 quarters.

Step-by-step explanation:

Represent the number of dimes and the number of quarters by d and q.

Then d + q = 15, or q = 15 - d.

Also, ($0.25) q + ($0.10) d = $2.85, or 5q + 2d = 57.

Substituding 15 - d for q, we get 5 (15 - d) + 2d = 57, or

75 - 5d + 2d = 57, or

75 - 3d = 57, or

3d = 18. Thus, there are 6 dimes. Since q = 15 - d, q = 15 - 6 = 9.

There are 6 dimes and 9 quarters.