Step 1 :Let x be the number of dimes and y be the number of quarters.
Step 2 :We have two equations: \(x + y = 11\) (total number of coins) and \(0.10x + 0.25y = 1.85\) (total value of the coins).
Step 3 :Solve the system of equations using substitution or elimination method.
Step 4 :Solution: \(x = 6\) and \(y = 5\).
Step 5 :\(\boxed{\text{Zachary has 6 dimes and 5 quarters}}\)