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Carpet price problem

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Carpet price problem

by Sampits » Sat Mar 20, 2010 11:33 am
Hi Experts,

I have another question for you guys, this is the problem:

"A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $50. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)

The answer is 450/xy... but I have a doubt...

My reasoning:

Price of the carpte in square feet: 50/xy

If we want it in square yard:

(50/xy)*(square feet)*(1 square yard/ 9 square feet)= (50/xy)*(1/9)*(square yard)= (50/9xy)!!!

Do you have any idea what I am doing wrong?

Thanks in advance,

MS
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by kstv » Sat Mar 20, 2010 4:56 pm
"A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $50. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)
Price of the carpte in square feet: 50/xy

Literally it means that the price of a square piece of carpet measuring 1 feet X 1 feet is $50/xy

If we want it in square yard, it is a larger square.
Each side of the square is now 3 feet (1 yard = 3 feet).
The area of the square is 3 feet X 3 feet = 9 sq. feet.
How many 1 sq. feet can you fit in this 9 sq. feet.

Should you divide 50/xy by 9 or multiply ?
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by this_time_i_will » Sun Mar 21, 2010 6:23 am
Sounds some what simple one, hopefully am not missing anyhting.

9Ft.^2 = 1Yd.^2.

Cost of xy Ft.^2 = 50$
Cost of 1 Ft. ^2 = 50/xy $
Cost of 9 Ft.^2 = (50/xy) * 9 = 450/xy $ = Cost of 1 Yd.^2.
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by Sampits » Sun Mar 21, 2010 10:28 am
Hi,

Now I know what I did wrong:

This is what I typed:

(50/xy)*(square feet)*(1 square yard/ 9 square feet)= (50/xy)*(1/9)*(square yard)= (50/9xy)!!!

And if we are talking about dollars per square feet, the right formula is:

(50/xy)*(1/square feet)*(9 square feet/ 1 square feet)= (50/xy)*(9)*(square yard)= (450/xy)!!!

Thank you both!

MS
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by acemans » Wed Aug 18, 2010 8:34 am
it would be simpler if we simply put in the conversion in the equation we created

we know that 9 sq ft = 1 sq yd

so xy sq ft = (xy/9) sq yds

and given is that $50 for xy sqft and the xy in terms of yards is xy/9 sq yds

so it can be written as $50/xy sqft and 50/(xy/9) sq yds

bring it up 9* $50/xy , the price in terms of yards = $ 450/xy /sq yds
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