Why is 9 involved in this problem instead of 3?

So, lets say it costs $1.25 per square yard to paint a wall. The wall is 18x25 feet. How much will it cost to paint the wall. First, I don't understand what is better. Converting 18x25 feet into yards which is (54x75) or converting down the cost from yard to feet which is aprox$0.416.

But lets say that it's better to convert feet to yards in this situation.

X is the cost.

X=((54*75)/9)*1.25

But again. There are 3 feet in a yard, and it looks like that 9 is squared. But I fail to understand why it's that way.

Can anyone explain? Thanks!

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Tip: Draw a picture of the situation –  Listing May 20 '11 at 10:09
Dimensional analysis (i.e., "check your units") is a good idea even in mathematics. –  ShreevatsaR May 20 '11 at 10:34
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1 Answer

The wall is not 18 x 25 feet. The wall is 18 feet x 25 feet, which is 18 x 25 square feet.

Converting 18 x 25 square feet into square yards does not give 54 x 75 square yards. Yards are bigger than feet. 18 feet, that's not 54 yards, it's 6 yards. 18 x 25 square feet give 6 x (25/3) square yards.

So the cost is 6 x (25/3) x \$1.25, whatever that comes to.

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