Fly-by-Night Airlines has a peculiar set of rules about luggage: 1) the length L

Question

Fly-by-Night Airlines has a peculiar set of rules about luggage:

1) the length L and width W of a bag must add up to at most 54 inches, and

2) the width W and height H must also add up to at most 54 inches.

What are the dimensions of the bag with the largest volume that Fly-by-Night will accept?

The Steps toward the Solution

Before you answer the question, break the problem information into smaller steps and calculations.

First, you notice that W, the width, is used in both rules. Let's use that fact to set up some useful equations. Let x be a variable that measures the width in inches. That is, W and x both measure the same quantity.

Note: Use only the case of the variables already shown in the above instructions.

a) If the width and the height add up to 54 inches, write an equation to express H in terms of the variable x only. = __________
      
b) If the length and the width add up to 54 inches, write an equation to express L in terms of the variable x only. = ___________
      
c) If the variable V determines the volume, write an equation for V in terms of the variables L, W, and H only. =_____________
      

Explanation / Answer

given the length L and width W of a bag must add up to at most 54 inches L + W = 54

the width W and height H must also add up to at most 54 inches W + H = 54

Let x be a variable that measures the width in inches

H in terms of the variable x is H = 54- x

L in terms of the variable x is L = 54- x

V determines the volume V = (54- x)2 x

the dimensions of the bag with the largest volume that Fly-by-Night will accept are 28, 26 and 28.

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