2004 Fermat Problem 19

A computer software retailer has 1200 copies of a new software package to sell. From past experience, she knows that:

- Half of them will sell right away at the original price she sets, - Two-thirds of the remainder will sell later when their price is reduced by 40%, and - The remaining copies will sell in a clearance sale at 75% off the original price.

In order to make a reasonable profit, the total sales revenue must be \$72\,000. To the nearest cent, what original price should she set?

\textbf{(A)}\ \$60.01\quad \textbf{(B)}\ \$75.01\quad \textbf{(C)}\ \$79.13\quad \textbf{(D)}\ \$80.90\quad \textbf{(E)}\ \$240.01

If there are no answer choices shown, enter a numerical answer.

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