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The formula you need is

Sq ft / 9 x cost = sq yds X cost = total bill so 150 /9 = 16.67 X 25 = $416.75

*Due to rounding of significant figures, this is more than the actual $ 416.67

which results from multiplying first.

150 * 25 / 9 = 3750 / 9 = 416.666

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Q: How much would it cost if you need 150 square feet of carpet and the cost of carpet per square yard is 25?
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