# algebra

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A rectangular box has Dimensions 16 inches and 22 inches and volume 4224 cubic inches. If the same amount is decreased from the largest and smallest sides, the volume of the new box is 6/11 of the first box. Find the dimensions of the second box.

• algebra -

original :
16 by 22 by x

352x = 4224
x = 12

So the first box is 22 by 16 by 12

let the amount decreased by y , clearly y < 12

then (22-y)(16)(12-y) = (6/11)(4224)
16(352 - 34y + y^2) = 2304
y^2 - 34y + 352 = 144
y^2 - 34y + 208 = 0
(y-26)(y-8) = 0 , but y < 12

so y = 8

so the second box is 14 by 16 by 4

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