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.

$$answer\ is\ Option\ D$$

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.

$$answer\ is\ Option\ D$$

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.