abhi758 wrote:
If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4 dollars and 4 pounds is equivalent to 56 crowns, 1 pound and 28 crowns is equivalent to how many dollars?
$7.00
$7.50
$8.50
$9.00
$10.00
\(?\,\,\,:\,\,\,p + 28c = f\left( d \right)\)
\(\left( {\rm{I}} \right)\,\,5d + 35c = 7p\)
\(4d + 4p = 56c\,\,\,\, \Rightarrow \,\,\,\,\left( {{\rm{II}}} \right)\,\,d + p = 14c\)
\(\left\{ \matrix{
2 \cdot \left( {\rm{I}} \right)\,\,\,\,10d + 70c = 14p\,\,\, \hfill \cr
5 \cdot \,\left( {{\rm{II}}} \right)\,\,\,5d + 5p = 70c \hfill \cr} \right.\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,15d = 9p\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,p = {5 \over 3}d\,\,\,\,\left( {{\rm{III}}} \right)\)
\(\left\{ \matrix{
\left( {\rm{I}} \right)\,\,\,\,5d + 35c = 7p\,\,\, \hfill \cr
7 \cdot \,\left( {{\rm{II}}} \right)\,\,\,7d + 7p = 98c \hfill \cr} \right.\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,12d = 63p\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,c = {4 \over {21}}d\,\,\,\,\left( {{\rm{IV}}} \right)\)
\(?\,\,:\,\,\,p + 28c\,\,\,\mathop = \limits^{{\text{III}}\,,\,\,{\text{IV}}} \,\,\,\,\frac{5}{3}d + 28\left( {\frac{4}{{21}}d} \right) = \frac{5}{3}d + \frac{{16}}{3}d = 7d\,\,\,\,\, \Rightarrow \,\,\,\,\boxed{\,\,? = \$ 7\,\,}\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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Fabio Skilnik ::
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