SOLUTION: The length of the Serumore Hotels lobby exceeds its width by 4 feet. A rug covers the floor of the lobby except for a border 2 feet wide all around it. If the area of this border

Question 316920: The length of the Serumore Hotels lobby exceeds its width by 4 feet. A rug covers the floor of the lobby except for a border 2 feet wide all around it. If the area of this border of exposed floor is 68 square feet, what is the are of the rug?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

represent the width of the lobby. Then

must represent the length of the lobby.

The width dimension of the rug must then be 4 feet less than the width of the room because there is a 2 foot border on each side. Likewise, the length dimension of the rug has to be 4 feet less than the length of the room. Hence the width of the rug is

and the length of the rug is

.

The total area of the room is:

And the total area of the rug is:

Now, if you subtract the area covered by the rug from the total area of the floor you should have the area of the uncovered border remaining.

So 8.5 feet for the width of the lobby, hence the width of the rug is 4.5

And 12.5 feet for the length of the lobby, hence 8.5 for the length of the rug.

Check:

Swish -- nothin' but net -- never a doubt. Under the category of "Does this make sense" note that this is a VERY small room for a hotel lobby. Once you put in a registration desk, there would hardly be anywhere for either the clerk or the arriving/departing guests to stand and conduct business. I would suspect that this is really a foyer leading to the larger lobby.

Also note a rather curious aspect of this problem. I generally advise students to make their initial assignment of the variable(s) to the quantity(ies) asked for by the problem. This particular problem was constructed in such a way that it would have required two variables and made the problem much more complex if you followed that advice.

John

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