Question

Suzanne went to the bank and withdrew 800. The teller gave her this amount using 20 bills, 50 bills, and 100 bills, with at least one of each denomination. How many different collections of bills could Suzanne have received?

Answer 1

Suzanne could have received 14 different collections of bills.

Explanation:

There are several ways Suzanne could have received a total of 800 dollars in 20s, 50s, and 100s. To find the possible combinations, let's consider the maximum number of each bill that Suzanne could have received. If she received the maximum number of 100s, which is 8 (800/100), then the remaining amount to be covered with 20s and 50s is 0. In this case, the possible combinations for 20s and 50s are (0, 16), (2, 14), (4, 12), (6, 10), (8, 8), (10, 6), (12, 4), (14, 2), (16, 0), where the first number represents the number of 20s and the second number represents the number of 50s. This gives us a total of 9 combinations.

Next, if Suzanne received the maximum number of 50s, which is 16 (800/50), then the remaining amount to be covered with 20s and 100s is 0. In this case, the possible combinations for 20s and 100s are (0, 8), (2, 6), (4, 4), (6, 2), (8, 0), giving us 5 combinations.

Finally, if Suzanne received the maximum number of 20s, which is 40 (800/20), then the remaining amount to be covered with 50s and 100s is 0. In this case, the possible combinations for 50s and 100s are (0, 8), (2, 6), (4, 4), (6, 2), (8, 0), giving us another 5 combinations.

Therefore, the total number of different collections of bills is 9 + 5 + 5 = 19. However, we need to subtract 5 from this total as one combination (0, 0, 8) is counted twice. Thus, Suzanne could have received 14 different collections of bills.