Problem of the Week - Upper Elementary - May 2, 2021 to May 8, 2021

Upper Elementary: 

Question: Tara gets to draw one bill at random from either of two buckets. One bucket has 30 $1 bills and 2 $100 bills. Another bucket has 80 $1 bills and 4 $100 bills. Which bucket should Tara choose? Why? 

Answer: Tara should choose the bucket with 30 $1 bills and 2 $100 bills. 

Solution: Since 2 out of 30 + 2 = 32 bills in the first bucket are $100 bills, that means that 2/32 = 1/16 of the bills are $100. In the other bucket, 4 out of 80 + 4 = 84 bills are $100, so 4/84 = 1/21 bills are $100. Since the first bucket has the greater fractional part comprising $100 bills, that is the smarter bucket to choose.