amitdgr wrote:
A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?
A. 3xr/2
B. 3x/200r
C. 3r/200x
D. 3xr/200
E. xr/600
Let´s avoid exploring particular cases (undoubtedly very useful) to embrace
UNITS CONTROL, one of the most powerful tools of our method!
\(\frac{{r\,\,{\text{cents}}}}{{1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\,\,\,\,\,\mathop \to \limits^{{\text{discount}}} \,\,\,\,\,\,\,\frac{{\frac{r}{2}\,\,{\text{cents}}}}{{1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\,\,\,\, = \,\,\,\,\,\frac{1}{2}\,\,\frac{{r\,\,{\text{cents}}}}{{\,\,1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\)
\(?\,\,\,:\,\,\$ \,\,{\text{for}}\,\,3\,\,{\text{people}}\,\,{\text{for}}\,\,x\,\,{\text{miles}}\,\,\,\left( {{\text{with}}\,\,{\text{discount}}} \right)\)
\(?\,\,\, = \,\,\,3\,\,{\text{person}}\,\,\, \cdot \,\,\,x\,\,{\text{miles}}\,\,\,\left( {\,\frac{1}{2}\,\,\frac{{r\,\,{\text{cents}}}}{{\,\,1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\,} \right)\,\,\,\left( {\frac{{1\,\,\$ }}{{100\,\,{\text{cents}}}}} \right)\,\,\,\,\, = \,\,\,\,\,\,\$ \,\,\,\frac{{3xr}}{{200}}\,\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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Fabio Skilnik ::
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