Use one equation for the number of coins and another equation for the value of the coins.
Let d = number of dimes.
Let q = number of quarters.
Number of coins:
q = 3d
Value of the coins:
A dime is worth $0.1
A quarter is worth $0.25
0.1d + 0.25q = 19.55
Now solve the two equations as a system of equations.
q = 3d
0.1d + 0.25q = 19.55
Since the first equation is already solved for q, replace q with 3d in the second equation.
0.1d + 0.25(3d) = 19.55
0.1d + 0.75d = 19.55
0.85d = 19.55
d = 23
q = 3d = 3(23) = 69
There are 23 dimes and 69 quarters.
Check:
23 dimes are worth 23 * $0.1 = $2.30
69 quarters are worth 69 * $0.25 = $17.25
The total value is $2.30 + $17.25 = $19.55
Also 69 is 3 times 23, so the number of quarters is indeed three times the number of dimes.
Our answer is correct.