### 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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## Comments

Didn't need a calculator a little too easy for me OK teaser though

I love math so I got it fairly easy. But I thought it was a great teaser.

ah i havent done school in weeks,im not realy computing math right now, i might get it right in a couple of months when my brain is working again LOLZ

WOW i didnt even see the calculator,Im am so stupid LOLZ

I love math and the fact I didn't even need the clue! Loved it!

i love this kinda thing keep playin this one cause i loved it!!!!

Easy! But, by the way, you copied this from a Eduplace math challenge question.

A book*case* with two shelves in it, each 15" high (which I assume means the space between the shelf and whatever is above/below it), would be 45" high (+ the thickness of the shelves). You would be able to accommodate 288 CDs in a 3' bookcase with only one shelf; with two, there's room for 432.

This is a response to lldhund...

True, if there's 2 shelves in a bookcase, there would be 3 open spaces. Does this mean each space is 15 in high? No, we only know that 2 are. The last space could be 6 in high. Or 26. Maybe changing the question would make it clearer. Still liked it, though!

True, if there's 2 shelves in a bookcase, there would be 3 open spaces. Does this mean each space is 15 in high? No, we only know that 2 are. The last space could be 6 in high. Or 26. Maybe changing the question would make it clearer. Still liked it, though!

You didn't say all the CDs had to go in the racks, just that all have to go in the bookcase. Just using the two shelves you can store at least 306 CDs.

Given the dimensions of the racks, a CD can be at most 7/12 of an inch thick and 17/3 inches wide.

This means there is space on top of the second rack on each shelf to store one more CD high x 3 wide. On the end there is 2 inches to spare, which can accomodate at least 2 / (7/12) = 3 CDs standing on their sides. 15 inches tall means that at least two rows of CDs on the end are possible.

This gives

144 + 3x1 + 3x2 = 153 per shelf

or 306 total.

Given the dimensions of the racks, a CD can be at most 7/12 of an inch thick and 17/3 inches wide.

This means there is space on top of the second rack on each shelf to store one more CD high x 3 wide. On the end there is 2 inches to spare, which can accomodate at least 2 / (7/12) = 3 CDs standing on their sides. 15 inches tall means that at least two rows of CDs on the end are possible.

This gives

144 + 3x1 + 3x2 = 153 per shelf

or 306 total.

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