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?
Mr. Klecak could have received a total of 41 bills.
To find the fewest number of bills, we prioritize the highest denomination first. By maximizing the number of $50 bills, we can minimize the total count of bills needed to reach $1,975.
This option indicates that Mr. Klecak would have received fewer bills than possible. If we tried to use only $50 bills, he could have received 39 bills ($1,950), requiring an additional $25, which cannot be made with the given denominations. Therefore, 38 bills is not achievable.
This is the correct answer. By receiving 39 $50 bills ($1,950) and 1 $20 bill ($20), plus 1 $5 bill ($5), Mr. Klecak receives a total of 41 bills. This combination effectively sums to $1,975 while minimizing the count of bills.
Receiving 44 bills implies a higher total than necessary. If we were to use more lower denominations, such as $20 and $5 bills, it would require more bills to make $1,975 while not achieving the minimum possible count. This suggests that 44 bills exceed the required number.
This option suggests an even larger number of bills than 44. It is impossible to reach the amount of $1,975 with such a high count of bills, as it would necessitate using too many small denominations, thus increasing the total count unnecessarily.
To minimize the number of bills Mr. Klecak received, strategically using higher denominations is key. The combination of 39 $50 bills, 1 $20 bill, and 1 $5 bill totals 41 bills, effectively meeting the target amount of $1,975 while ensuring the fewest possible bills. Therefore, the answer is 41.
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