A department store stocks gift boxes for the holiday season. The box has a volume of 500 cubic inches. You also know that the length of the box is 9 inches longer than the width and the height 1/2 as long as the width

31.6in

Step-by-step explanation:

A department store stocks gift boxes for the holiday season. The box has a volume of 500 cubic inches. You also know that the length of the box is 9 inches longer than the width and the height 1/2 as long as the width

Volume of the box = Length * Width * Height

Given

Volume = 500in³

If the length of the box is 9 inches longer than the width, then;

L = W+9

Also if the height is 1/2 as long as the width, then;

H = 1/2 W

Substtute into the volume formula;

V = LWH

500 = (W+9)W(1/2W)

500 = W+9(W²/2)

1000 = W²(W+9)

1000 =W³+9W²

W³+9W² - 1000 = 0

Factorize AND GET w

W³+9W² = 1000

w²(W+9) = 1000

W² = 1000

w = √1000

w = 31.6in

Hence the width of the store is 31.6in

Note that we only looked for the width since are not told what to find

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step-by-step explanation: