Let x gallons be the amount of pure antifreeze that should be added to the 30% solution to produce a solution that is 65% antifreeze. Then the total amount of antifreeze solution will be x+3 gallons.
There are 30% of pure antifreeze in 3 gallons of solution, then
3 gallons - 100%,
a gallons - 30%,
where a gallons is the amount of pure antifreeze in given solution.
Mathematically,
[tex]\dfrac{3}{a}=\dfrac{100}{30},\\ \\a=\dfrac{3\cdot 30}{100}=0.9\ gallons.[/tex]
Now in new solution there will be x+0.9 gallons of pure antefreeze.
x+3 gallons - 100%,
x+0.9 - 65%
or
[tex]\dfrac{x+3}{x+0.9}=\dfrac{100}{65},\\ \\65(x+3)=100(x+0.9),\\ \\65x+195=100x+90,\\ \\35x=105,\\ \\x=3\ gallons.[/tex]
Answer: he should add 3 gallons of pure antifreeze.
