### Brain Teasers

# Soup Cans

Adoontourious designs food displays for the Nile Supermarket chain. For one of his displays, he wants to set up soup cans in the form of a square pyramid. He's decided to use 9 cans for each side of the square base of the pyramid.

If each carton holds 24 soup cans, how many cartons will adoontourious need to open to build the pyramid?

If each carton holds 24 soup cans, how many cartons will adoontourious need to open to build the pyramid?

### Answer

Adoontourious will need to open 12 cartons.The 9-by-9 square base of the pyramid will have 81 cans. Building upward, the next layer will have 8 x 8, or 64 cans. The next layer will have 7 x 7, or 49 cans, and so on up to the top layer (which will have just 1 can). Add the cans in all 9 layers, and you'll find that the total number of cans needed to build the pyramid is 285.

Divide the total number of cans by the number of cans in a carton : 285 ÷ 24 = 11.87. Since adoontourious can't open 11.87 cartons, he'll have to open 12 cartons : 12 x 24 = 288. Then he'll be left with 3 extra cans!

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