algebra
posted by Rose
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.

Reiny
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 (22y)(16)(12y) = (6/11)(4224)
16(352  34y + y^2) = 2304
y^2  34y + 352 = 144
y^2  34y + 208 = 0
(y26)(y8) = 0 , but y < 12
so y = 8
so the second box is 14 by 16 by 4
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