AMC 10 Daily Practice Round 1
Complete problem set with solutions and individual problem pages
You have four bills each of denominations 1 dollar, 2 dollars, and 5 dollars. How many different ways can you use these bills to make a total of 23 dollars?
- A.
- B.
- C.
- D.
- E.
To pay 23 dollars, we can use up to 4 bills of 5 dollars each. Since using all 1-dollar and 2-dollar bills totals 12 dollars, at least 3 bills of 5 dollars must be used. When using 3 bills of 5 dollars, the total value of the 5-dollar bills is dollars, leaving dollars to be made up with 1-dollar and 2-dollar bills. We can use the 2-dollar bills as follows: giving us 3 different payment methods. When using 4 bills of 5 dollars, the total value is dollars, leaving dollars. We can pay this using: giving us 2 more payment methods. Therefore, the total number of distinct payment methods is .
