Reader Submission #18

Question:

Axel and Brady had some identical large cubes and some identical small cubes. Each of them had a rectangular box of the same base but different height. They packed their cubes into their own box with cubes of the same size stacked on top of each other.

The figure below shows the first layer of cubes packed in each box.

a) Axel’s box was packed tightly to the brim without any gaps. There were 50 more small cubes than large cubes. How many cubes were packed into the box altogether?

b) In Brady’s box, the space occupied by all the large cubes and that of the small cubes was the same. What fraction of the cubes was the small cubes?