62. Mr. Klecak cashed his check for $1,975 at the bank and asked to receive only $50 bills, $20 bills, and $5 bills. What is the fewest number of bills he could have received?
Answer: B
Mr. Klecak could have received 41 bills.
To determine the fewest number of bills Mr. Klecak could have received, we can optimize the denominations he requested. By prioritizing higher denominations first, we can minimize the total number of bills.
A) 38
This option suggests that Mr. Klecak could have received only 38 bills. However, if we calculate using the largest denominations first, achieving a total of $1,975 with 38 bills is not feasible. The distribution of bills would not allow for this total in the denominations requested.
B) 41
This is the correct answer. By using 39 $50 bills (totaling $1,950) and 1 $20 bill (totaling $20), Mr. Klecak would have 40 bills, plus an additional $5 bill to sum to $1,975, leading to a total of 41 bills. This method uses the highest denomination effectively to minimize the total number of bills.
C) 44
This option indicates that Mr. Klecak received 44 bills. To achieve this total, he would need to use a combination of lower denominations without maximizing the use of $50 bills, which contradicts the goal of minimizing the number of bills. Therefore, this option is incorrect.
D) 53
This choice implies that Mr. Klecak received 53 bills, which is more than necessary. With the given denominations, it is possible to reach $1,975 with fewer bills. Thus, this option does not align with the objective of obtaining the fewest bills possible.
Conclusion
The answer of 41 bills is confirmed as the minimal count necessary for Mr. Klecak to receive his total of $1,975 when utilizing the denominations of $50, $20, and $5. The other options fail to reach the total with fewer bills, making them less efficient and incorrect.