Bunuel wrote:

The selling price of an article is equal to the cost of the article plus the markup. The markup on a certain television set is what percent of the selling price?

(1) The markup on the television set is 25 percent of the cost.

(2) The selling price of the television set is $250.

\({\text{sell}} = {\text{cost}} + {\text{mark}}\,\,\,\,\left( * \right)\)

\(\left[ {{\text{mark}} = \frac{x}{{100}}\left( {{\text{sell}}} \right)\,\,\,\, \Rightarrow } \right]\,\,\,\,\,\,\,?\,\, = \,\,100 \cdot \frac{{{\text{mark}}}}{{{\text{sell}}}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\boxed{?\,\, = \frac{{{\text{mark}}}}{{{\text{sell}}}}}\,\,\)

\(\left( 1 \right)\,\,\,\frac{1}{4} = \frac{{{\text{mark}}}}{{{\text{cost}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{{\text{mark}}}}{{{\text{sell}} - {\text{mark}}}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{{\text{sell}} - {\text{mark}}}}{{{\text{mark}}}} = 4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{{\text{sell}}}}{{{\text{mark}}}} - 1 = 4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\,\, = \,\,{\left( {\frac{{{\text{sell}}}}{{{\text{mark}}}}} \right)^{ - 1}}\,\,\, = \frac{1}{5}\)

\(\left( 2 \right)\,\,\,{\text{sell}} = 250\,\,\,\left\{ \begin{gathered}

\,{\text{If}}\,{\text{cost}} = 200\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,{\text{mark}} = 50\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{{50}}{{250}} = \frac{1}{5}\,\, \hfill \\

\,{\text{If}}\,{\text{cost}} = 150\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,{\text{mark}} = 100\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{{100}}{{250}} \ne \frac{1}{5}\,\, \hfill \\

\end{gathered} \right.\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,

fskilnik.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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