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The total cost of carpeting a rectangular room is given the expression $$6x^2 + 18x$$ Which situation best describes the expression?

  1. The length of the room is 6+2x feet, its width is 2x feet, and the cost of carpeting is $1.50per square foot.

  2. The length of the room is 3 + 2x feet, its width is 2x feet and the cost of carpentering is $3.00 per square foot

  3. The area of the floor is $$4x^2 + 9x$$ square feet, and the cost of carpeting is $1.50 per square foot.

  4. The area of the floor is $$ 2x^2 + 9x$$ square feet, and the cost of carpeting is $3.00 per square foot.

The first thing I did to try to solve this was I factored it so $$6x(x + 3)$$ so area is found by doing L * W so which one would be the length 6x or (x+3). Cause I mean it can be anyone of these. Which is the correct answer from the given? and also could you explain why?

MATH ASKER
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1 Answers1

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Consider the first situation $$(6+2x)\times (2x)\times 1.5=6 x^2+18 x$$ Consider the second situation $$(3+2x)\times (2x)\times 3=12 x^2+18 x$$ Consider the third situation $$(4x^2+9x)\times 1.5=6 x^2+\frac{27 }{2}x$$ Consider the fourth situation $$(2x^2+9x)\times 3=6 x^2+27 x$$ Hoping no mistake.

For this kind of problem, just consider the different cases; may be two (or more) could be equivalent.

Happy New Year !!

Claude Leibovici
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