### Brain Teasers

# Stacking CD's

Andrew has a new 3 foot wide bookcase with two shelves, each 15 inches high. He plans to store his CD's on the shelves using new CD racks. Each CD rack is 17 inches wide and 7 inches high, and holds 3 stacks of 12 CD's.

Will Andrew have enough room for his 250 CD's in the bookcase if he uses the two shelves inside the bookcase and doesn't put any CD's on top of it? How many CD's will he be able to store?

Will Andrew have enough room for his 250 CD's in the bookcase if he uses the two shelves inside the bookcase and doesn't put any CD's on top of it? How many CD's will he be able to store?

### Hint

Drawing a diagram may be helpful.### Answer

Yes, Andrew will have enough room on the two shelves to fit his 250 CD's. In fact, he will be able to fit up to 288 CD's.Each CD rack holds 36 CD's. (12 x 3 = 36)

Each shelf is 3 feet or 36 inches wide, and therefore wide enough to hold 2 CD racks. (2 x 17 = 34)

Each shelf is 15 inches high, and therefore high enough to hold 2 layers of CD racks. (2 x 7 = 14)

Therefore, each shelf holds 4 CD racks, or 36 x 4 = 144 CD's.

There are two shelves, each holding 144 CD's, or 288 CD's in all.

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