Let's use a system of two equations to solve this problem:
Let:
q be the number of quarters
d be the number of dimes
From the problem, we know that:
Equation 1: q + d = 38 (the total number of coins is 38)
Equation 2: 0.25q + 0.1d = 6.35 (the total value of the coins is $6.35)
To solve for q and d, we can use substitution or elimination. Let's use substitution:
From Equation 1, we can solve for q:
q = 38 - d
Substitute this expression for q into Equation 2:
0.25(38 - d) + 0.1d = 6.35
Simplify and solve for d:
9.5 - 0.25d + 0.1d = 6.35
-0.15d = -3.15
d = 21
Substitute this value of d back into Equation 1 to solve for q:
q + 21 = 38
q = 17
So there are 17 quarters and 21 dimes.