COOKIES FOR DESSERT

a) Three algebra students were doing their homework together. As a treat, one mom offered to bake some cookies. While waiting for them to cool, all three students fell asleep. After a while, Latisha woke up, ate her equal share of cookies and went back to sleep. A little while later, Susan woke up, ate what she thought was her equal share and fell asleep again. Then Hieu woke up, ate what she thought was her equal share, and went back to sleep. Later, all three kids woke up and discovered 8 cookies left.

How many cookies were baked originally?

b) The next day, four students got together to study. Another mom baked cookies. Again the four students fell asleep. As before, they woke up one at a time and each ate her equal share. When they all awakened, they discovered 81 cookies remained.

How many cookies were baked originally?

Your Task:

(1) Solve both problems.

(2) Compare the original cookie numbers to the final numbers of cookies left. What is their relationship?

(3) What would happen if there were 5 students? As before, each student ate her equal share of what was left. When they all awakened, how many cookies remained? How many cookies were baked originally?

(4) Explain how this problem would work for any number of students.