DivyaD wrote:Thor just filled his truck's gas tank with 20 gallons of a mixture consisting of 10% additive and 90% gasoline. If his truck runs best on a mixture consisting of 20% additive and 80% gasoline, how many gallons of additive must he add into the gas tank for his truck to achieve optimum performance?
a) 1.0
b) 1.5
c) 2.0
d) 2.5
e) 3.0
$$? = x\,\,\left( {{\rm{gallons}}\,\,{\rm{addit}}} \right)$$
$$20\,\,{\rm{gallons}}\,\,\,\left\{ \matrix{
\,{\rm{addit}}\,\,\,\, \to \,\,\,\,2\,\,{\rm{gallons}} \hfill \cr
\,{\rm{gasol}}\,\,\,\, \to \,\,\,\,18\,\,{\rm{gallons}} \hfill \cr} \right.$$
$${{2 + x} \over {18}} = {1 \over 4}\,\,\,\,\left( {{{20\% } \over {80\% }}} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,8 + 4x = 18\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = x = {{10} \over 4} = 2.5$$
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
