Collection of dimes and quarters has a total of $19.55. if there are three times as many quarters as dimes, find the number of each?

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.