In her wallet, Ms. Thompson has one-dollar, five-dollar, and ten-dollar bills, totally $171. She has the same number of five-dollar bills as one-dollar and ten-dollar bills put together. If she has 30 bills in all, how many bills of each denomination does she have?

Ms. Thompson has six one-dollar bills, fifteen five-dollar bills, and nine ten-dollar bills. Let the variables x, y, and z be the denominations of one, five, and ten bills, respectively. You can solve the values of the denominations through the following equations and with the use of substitution and elimination techniques:

a. y=x+z

b. x+y+z=30

c. x+5y+10z=171