Let t and h represent the number of twenty- and hundred-dollar bills given the crook, respectively.
.. 20t +100h = 10000 . . . . . . the total value of the payment was $10,000
.. t - h = 20 . . . . . . . . . . . . . . . she gave him 20 more twenties than hundreds
Using an augmented matrix, the solution can be found to be
.. t = 100
.. h = 80
She gave the crook only 100 20s, so did not meet the requirement for 105 twenty-dollar bills. Polly did not give him enough.