Al and Bob are just sitting down to lunch when they are joined by their friend Carol. Al has brought 5 sandwiches to eat, Bob has brought 3, but Carol has not brought any. She does have $4, however. The three of them divide the food evenly, and then Carol gives Al and Bob her $4 to pay for her share. How should Al and Bob share the money?
Since Al contributed 5/8 of the food and Bob contributed 3/8, Al should get 5/8 of the $4.00, or $2.50, and Bob should get 3/8, the remaining $1.50.
Oops, wait a minute. This solution would only apply if Al and Bob had given all of their sandwiches to Carol, but they didn’t. They both ate some of the sandwiches and gave the remainder to Carol. Since 3 people shared a total of 8 sandwiches equally, each of them ate 8/3 sandwiches. Thus Al contributed 5 – 8/3 = 7/3 sandwiches to Carol, and Bob contributed 3 – 8/3 = 1/3 sandwich. So Al should get 7/8 of the $4, or $3.50, and Bob should get 1/8, or $.50.
Stella thanks astute problem solver Ken Haley for catching the error in her solution — thanks, Ken!