Problem:
For his birthday, Bert gets a box that holds jellybeans when filled to capacity. A few weeks later, Carrie gets a larger box full of jellybeans. Her box is twice as high, twice as wide and twice as long as Bert's. Approximately, how many jellybeans did Carrie get?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since the exact dimensions of Bert's box do not matter, assume the box is . Its volume is . Carrie's box is , so its volume is or times the volume of Bert's box. Carrie has approximately jellybeans.
Note: Other examples may help to see that the ratio is always to .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions