James had a rectangular piece of cardboard that was four times as long as it was wide. He wanted to use the cardboard to make a box with no lid. To do this, he first cut a 3-by-3 inch square out of each of the four corners of the piece of cardboard, as shown in the picture below.

Then James folded the cardboard along the four dotted lines shown in the picture. This created an open box with a volume of 336 cubic inches. What was the width of the sheet of cardboard that james started with?

Question

James had a rectangular piece of cardboard that was four times as long as it was wide. He wanted to use the cardboard to make a box with no lid. To do this, he first cut a 3-by-3 inch square out of each of the four corners of the piece of cardboard, as shown in the picture below.

Then James folded the cardboard along the four dotted lines shown in the picture. This created an open box with a volume of 336 cubic inches. What was the width of the sheet of cardboard that james started with?

anonymous · Answer

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cwrw238 · Answer

let x be width then 4x is the length
now make an expression  for the volume of the box in terms of x  and equate it to 336
solve this to find x

anonymous · Answer

Okay so (4x)(x)(3)=336 or do you have to subtract the corners so (4x-6)(x)(3)=336?

cwrw238 · Answer

hint: the width of the box will be ( x - 6 ) inches
so what is the length?

anonymous · Answer

4x-24?

cwrw238 · Answer

no  - you were correct with the length the first time  its 4x - 6

anonymous · Answer

Oh okay. woops. so then it would be L*W*H (3x-6)(x-6)(3)=336?

cwrw238 · Answer

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