Explanation

If we call the price of the item sold P, then the excess of $9,000 of the price is . Whenever writing an algebraic expression such as this, if you can think of a concrete example on hand to try, that's an easy way to confirm that your algebra is correct. For example, if the price were 10,000, then and and it all makes sense, so the expression is correct. We're told 9% of this amount is Pat's commission, so we have the equation



We must solve for P. It's worth checking the answer choices; maybe plugging one in would be much easier than solving for the answer, but probably not in this case.



We can convert decimals into fractions, because math with fractions has ample opportunities to simplify.





There is a divisibility by 9 trick: if the digits of a number add to 9, the number is divisible by 9, so 405 (4 + 0 + 5 = 9) is divisible by 9.







We have our answer. We can double-check that it makes sense: the amount in excess of $9,000 is $4,500, and her commission was a bit less than 10%, so a bit less than $450, so $405 makes sense. The correct answer is (C).