A package in the shape of a rectangular solid is to be mailed. The combination of the girth (perimeter of a cross section defined by w and h) and the length of the package is 60 in. The width is 4 in. greater than the height, and the length is 13 in. greater than the width. Find the dimensions of the package.

9514 1404 393

Step-by-step explanation:

The problem statement tells us that the length (l), width (w), and height (h) are related by ...

  2(w+h) +l = 60

  w = h +4

  l = w +13

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Substituting for l, we get ...

  2(w +h) +(w +13) = 60

Then substituting for w, we have ...

  2((h +4) +h) +((h +4) +13)) = 60

  5h +25 = 60

  5h = 35

  h = 7

  w = 7 +4 = 11

  l = 11 +13 = 24

The package is 7 in high, 11 inches wide, and 24 inches long.