dwag wrote:

For each customer, a bakery charges p dollars for the first loaf of bread bought by the customer and charges q dollars for each additional loaf bought by the customer. What is the value of p ?

(1) A customer who buys 2 loaves is charged 10 percent less per loaf than a customer who buys a single loaf.

(2) A customer who buys 6 loaves of bread is charged 10 dollars.

\({\text{\$ }}p\,\,\,:\,\,{\text{first}}\,\,{\text{loaf}}\)

\({\text{\$ }}q\,\,\,{\text{:}}\,\,\,{\text{any}}\,\,{\text{additional}}\,\,{\text{loaf}}\)

\(? = q\)

\(\left( 1 \right)\,\,{\left( {\frac{{\,{\text{charge}}\,}}{{{\text{loaf}}}}} \right)_{\,2\,\,{\text{loaves}}}} = \frac{{p + q}}{2}\,\,\,\,\mathop = \limits^{{\text{given}}} \,\,\frac{9}{{10}}p\,\,\,\,\, \Rightarrow \,\,\,\, \ldots \,\,\,\,\, \Rightarrow \,\,\,\frac{q}{p} = \frac{4}{5}\)

\(\left\{ \begin{gathered}

\,{\text{Take}}\,\,\left( {p,q} \right) = \left( {0.5,0.4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 0.4 \hfill \\

\,{\text{Take}}\,\,\left( {p,q} \right) = \left( {1,0.8} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 0.8 \hfill \\

\end{gathered} \right.\)

\(\left( 2 \right)\,\,6\,\,{\text{loaves}}\,\,{\text{for}}\,\,\$ 10\,\,\,\left\{ \begin{gathered}

\,{\text{Take}}\,\,\left( {p\,;q} \right) = \left( {2\,;\frac{8}{5}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{8}{5} \hfill \\

\,{\text{Take}}\,\,\left( {p\,;q} \right) = \left( {3\,;\frac{7}{5}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{7}{5} \hfill \\

\end{gathered} \right.\)

\(\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered}

p + 5q = 10 \hfill \\

\frac{q}{p} = \frac{4}{5} \hfill \\

\end{gathered} \right.\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{k}}\,\,{\text{technique}}} \,\,\,\,\left( {5k} \right) + 5\left( {4k} \right) = 10\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 4k\,\,{\text{unique}}\,\)

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

Regards,

Fabio.

_________________

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

Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!