SOLUTION: Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 30 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 476 square feet of
Question 1196090: Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 30 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 476 square feet of carpeting. What dimensions should the rug have? Found 3 solutions by Alan3354, ikleyn, greenestamps:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 30 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 476 square feet of carpeting. What dimensions should the rug have?
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s = strip width
(19-s)*(30-s) = area of rug = 476
476 = 17*28
You can put this solution on YOUR website! .
Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 30 ft long.
She wants to leave a uniform strip of floor around the rug.
She can afford to buy 476 square feet of carpeting.
What dimensions should the rug have?
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The hint given by Alan needs to be presented in more precise and accurate form.
s = strip width
(19-2s)*(30-2s) = area of rug = 476
476 = 17*28
Get a quadratic equation for s.
Solve it by any way you want (use the quadratic formula or factoring).
After finding the strip width, calculate the dimensions of the rug.
To see many other similar (and different) solved problems
(including that about legendary Cynthia Besch), look into the lessons
The difference between the length and width of the room is 30-19=11 feet. Since the strip around the rug is to be of uniform width, the difference between the length and width of the rug must also be 11 feet.
So find how to factor 476 as the product of two integers whose difference is 11.
476 = 119*4 = 7*17*4 = 28*17
ANSWER: The rug should be 28 feet long and 17 feet wide.
For a formal algebraic solution, we can let x be the width of the uniform strip around the rug, making the dimensions of the rug 30-2x and 19-2x. Then, given the area of the rug as 476 square feet,
The width of the uniform strip is either 47/2 = 23.5 feet or 1 foot.
The 23.5 feet makes no sense, so the width of the strip is 1 foot, making the dimensions of the rug 28 feet by 17 feet.
But that algebraic solution was much harder than the informal solution shown earlier -- so the formal algebra doesn't give you an easier way to find the answer to the problem.
