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
Thor just filled his truck's gas tank with 20 gallons of a m
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20 gallons consist of 10% additives and 90% gasoline
$$10\%\ of\ 20=\frac{10}{100}\cdot20=2$$
2 gallons of additive and 18 gallons of gasoline
His tank runs bet at 20% additive and 80% gasoline
If 80% gasoline needs 20% additive
then 90%gasoline will need x% additive.
$$\frac{80x}{80}=\frac{1800}{80}$$ $$\frac{80x}{80}=\frac{1800}{80}$$
$$x=22.5\%\ of\ additive\ is\ needed\ for\ 90\%gasoline$$
We already have 10% additive, hence we only need to add (22.5-10=12.5%) of additive.
$$If\ 10\%=2\ gallons$$
$$12.5\%=\frac{\left(12.5\cdot2\right)}{10}=2.\ 5\ gallons$$
Thor must add 2.5 gallons of additive into the gas tank for his tank to achieve optimum performance.
$$answer\ is\ Option\ D$$
$$10\%\ of\ 20=\frac{10}{100}\cdot20=2$$
2 gallons of additive and 18 gallons of gasoline
His tank runs bet at 20% additive and 80% gasoline
If 80% gasoline needs 20% additive
then 90%gasoline will need x% additive.
$$\frac{80x}{80}=\frac{1800}{80}$$ $$\frac{80x}{80}=\frac{1800}{80}$$
$$x=22.5\%\ of\ additive\ is\ needed\ for\ 90\%gasoline$$
We already have 10% additive, hence we only need to add (22.5-10=12.5%) of additive.
$$If\ 10\%=2\ gallons$$
$$12.5\%=\frac{\left(12.5\cdot2\right)}{10}=2.\ 5\ gallons$$
Thor must add 2.5 gallons of additive into the gas tank for his tank to achieve optimum performance.
$$answer\ is\ Option\ D$$
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20 gallons consist of 10% additives and 90% gasoline
$$10\%\ of\ 20=\frac{10}{100}\cdot20=2$$
2 gallons of additive and 18 gallons of gasoline
His tank runs bet at 20% additive and 80% gasoline
If 80% gasoline needs 20% additive
then 90%gasoline will need x% additive.
$$\frac{80x}{80}=\frac{1800}{80}$$ $$\frac{80x}{80}=\frac{1800}{80}$$
$$x=22.5\%\ of\ additive\ is\ needed\ for\ 90\%gasoline$$
We already have 10% additive, hence we only need to add (22.5-10=12.5%) of additive.
$$If\ 10\%=2\ gallons$$
$$12.5\%=\frac{\left(12.5\cdot2\right)}{10}=2.\ 5\ gallons$$
Thor must add 2.5 gallons of additive into the gas tank for his tank to achieve optimum performance.
$$answer\ is\ Option\ D$$
$$10\%\ of\ 20=\frac{10}{100}\cdot20=2$$
2 gallons of additive and 18 gallons of gasoline
His tank runs bet at 20% additive and 80% gasoline
If 80% gasoline needs 20% additive
then 90%gasoline will need x% additive.
$$\frac{80x}{80}=\frac{1800}{80}$$ $$\frac{80x}{80}=\frac{1800}{80}$$
$$x=22.5\%\ of\ additive\ is\ needed\ for\ 90\%gasoline$$
We already have 10% additive, hence we only need to add (22.5-10=12.5%) of additive.
$$If\ 10\%=2\ gallons$$
$$12.5\%=\frac{\left(12.5\cdot2\right)}{10}=2.\ 5\ gallons$$
Thor must add 2.5 gallons of additive into the gas tank for his tank to achieve optimum performance.
$$answer\ is\ Option\ D$$
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$$? = x\,\,\left( {{\rm{gallons}}\,\,{\rm{addit}}} \right)$$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
$$20\,\,{\rm{gallons}}\,\,\,\left\{ \matrix{
\,{\rm{addit}}\,\,\,\, \to \,\,\,\,2\,\,{\rm{gallons}} \hfill \cr
\,{\rm{gasol}}\,\,\,\, \to \,\,\,\,18\,\,{\rm{gallons}} \hfill \cr} \right.$$
$${{2 + x} \over {18}} = {1 \over 4}\,\,\,\,\left( {{{20\% } \over {80\% }}} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,8 + 4x = 18\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = x = {{10} \over 4} = 2.5$$
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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