Home > Problem of the Week > Archive List > Detail

<< Prev 3/18/2007 Next >>

Tanner Takes the Cake

First, try this version....
Tanner had a birthday cake which had a top surface area of one square foot. He gave Taz 1/9 square foot of his birthday cake. He then gave Trampis 1/4 of what was left. After that, he gave Trey 1/3 of what was left. After that, he gave Talon, Ella, Garry and himself equal-sized pieces. How many square inches (surface area) of cake did each person get?

Now try this version?
Tanner had a birthday cake which had a top surface area of one square foot. He gave Taz all but 1/9 square foot of his birthday cake. He then gave Trampis all but 1/4 of what was left. After that, he gave Trey all but 1/3 of what was left. After that, he gave Talon, Ella, Garry and himself equal-sized pieces. How many square inches (surface area) of cake did each person get?

Finally, try this version?
Tanner had a birthday cake which had a top surface area of one square foot. He gave Taz 1/9 square foot of his birthday cake. He then gave Trampis 1/4 of the cake. After that, he gave Trey 1/3 of the cake. After that, he gave Talon, Ella, Garry and himself equal-sized pieces. How many square inches (surface area) of cake did each person get?

Do you see how the problems are the same yet different? Is one problem easier to solve than the others?

 


Hint: Draw a picture....the problem perhaps solved easier visually than it is using algebra.

 


Solution Commentary:

Note 1: You should discover that the answers to the three problems differ.

Note 2: You should find the first problem is the easiest to solve visually...why?

Note 3: You should find that the order of the cake-eaters (if ordered by size of cake portion--largest to smallest) will vary across the problems...but should they? In which situation would you like to be Tanner? In what case is Tanner like Ella? In what case is Trampis like Trey?