A dime is worth 10 cents and a quarter is worth 25 cents.
Let D be the number of dimes and Q be the number of quarters.
Since the total amount of coins in the pocket is 32, then:
On the other hand, the total value of D dimes is 10D, while the total value of Q dimes is 25Q. Then, the total value of D dimes and Q cuarters is 10D+25Q, which must be equal to 545. Then:
Notice that we have found a 2x2 system of equations:
Solve the system using the substitution method. To do so, isolate D from the first equation and replace the expression for D into the second equation to obtain a single equation in terms of Q:
Replace back Q=15 into the expression for D to find the amount of dimes:
Therefore, the amount of dimes that the man has is 17.