Bunuel wrote:
Amy, Betty, and Chris paid a total of $135 for a common party. If Amy paid (3/5)th of what Chris paid, Betty paid $51 and Chris paid the rest, what fraction of the total amount did Chris pay?
(A) 3/7
(B) 1/5
(C) 2/15
(D) 7/18
(E) 11/18
\(\left. \begin{gathered}
C = \$ \,5k \hfill \\
A = \$ \,3k\,\, \hfill \\
B = \$ 51 \hfill \\
\end{gathered} \right\}\,\,\,\,\,\,8k + 51 = 135\,\,\,\,\,\,\,\,\,\left( {k > 0} \right)\)
\(? = \frac{{5k}}{{135}}\,\mathop = \limits^{\left( * \right)} \,\,\frac{k}{{27}}\)
\(\left( * \right)\,\,\,\frac{{135}}{5} = \underleftrightarrow {\frac{{100}}{5} + \frac{{35}}{5}} = 27\,\,\,\,\, \Rightarrow \,\,\,\,\,135 = 5 \cdot 27\)
\(8k = \underleftrightarrow {135 - \left( {35 + 16} \right)} = 84\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits_{{\text{FOCUS}}\,\,!}^{:\,\,\left( {8\, \cdot \,27} \right)} \,\,\,\,\,\,\,\,? = \frac{{8k}}{{8 \cdot 27}} = \underleftrightarrow {\frac{{84}}{{8 \cdot 27}}} = \frac{{4 \cdot 3 \cdot 7}}{{8 \cdot 3 \cdot 9}} = \frac{7}{{18}}\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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