Let x = number of $1 bills, y = number of $5 bills and z = number of $10 bills.

Then:

x + y + z = 225 .... (1)

x + 5y + 10z = 596 .... (2)

x = 7z .... (3)

I suggest substituting (3) into (1) and (2) to eliminate x. Now solve (1) and (2) simultaneously for z and y. Now sub the value of x into (3) to get x.