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If the total price for n copies of a book is $31.5, what is

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If the total price for n copies of a book is $31.5, what is

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Source: Princeton Review

If the total price for n copies of a book is $31.5, what is the price per copy of the book?

1) If twice as many copies were bought for the same total price, the price per copy would be $1.75.
2) If 4 fewer copies were bought for the same total price, the price per copy would be $2.80 greater.

The OA is D.

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BTGmoderatorLU wrote:
Source: Princeton Review

If the total price for n copies of a book is $31.5, what is the price per copy of the book?

1) If twice as many copies were bought for the same total price, the price per copy would be $1.75.
2) If 4 fewer copies were bought for the same total price, the price per copy would be $2.80 greater.
$$? = c\,\,\left( {{\rm{dollar}}\,\,{\rm{cost}}\,\,{\rm{per}}\,\,{\rm{copy}}} \right)$$
$$n \cdot c = 31.5\,\,\,\,\left[ \$ \right]\,\,\,\,\,\,\left( * \right)$$
$$\left( 1 \right)\,\,2n \cdot 1.75 = 31.5\,\,\,\, \Rightarrow \,\,\,n\,\,{\rm{unique}}\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,? = c\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,{\rm{SUFF}}{\rm{.}}$$
$$\left( {\,{\rm{POST - MORTEM}}\,\,:\,\,\,\,c\,\,\mathop = \limits^{\left( * \right)} \,\,{{31.5} \over n} = 2 \cdot 1.75\,} \right)$$
$$\left( 2 \right)\,\,\left( {n - 4} \right)\left( {c + 2.8} \right) = 31.5\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\left( {{{31.5} \over c} - 4} \right)\left( {c + 2.8} \right) = 31.5$$
$$31.5 = 31.5 + {{\left( {31.5} \right)\left( {2.8} \right)} \over c} - 4c - 4 \cdot 2.8\,\,\,\,\, \Rightarrow \,\,\,\,\,4{c^2} + 4 \cdot 2.8 \cdot c - \left( {31.5} \right)\left( {2.8} \right) = 0$$
$${c_1}{c_2} = {{ - \left( {31.5} \right)\left( {2.8} \right)} \over 4} < 0\,\,\,\,\left( {{c_1},{c_2}\,\,{\rm{roots}}} \right)\,\,\,\,\, \Rightarrow \,\,\,c > 0\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,{\rm{SUFF}}.$$

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

Regards,
Fabio.

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