Question 147292
In words:
(amount of salt you end up with) / (total amount of solution) = % salt
Let {{{x}}} = amount of 70% solution to be added
How much salt is in the 20 liters of 40% solution?
{{{ .4 *20 = 8}}} liters
How much salt is in the 70% solution?
{{{.7x}}}
How much total solution do you end up with?
{{{20 + x}}}
So, the equation to use is:
{{{(8 + .7x) / (20 + x) = .5}}}
multiply both sides by {{{20 + x}}}
{{{8 + .7x = .5*(20 + x)}}}
{{{8 + .7x = 10 + .5x}}}
{{{.2x = 2}}}
{{{x = 10}}}
The chemist needs to add 10 liters of the 70% solution
check answer:
{{{(8 + .7x) / (20 + x) = .5}}}
{{{(8 + .7*10) / (20 + 10) = .5}}}
{{{(8 + 7) / 30 = .5}}}
{{{15/30 = .5}}}
{{{15 = .5*30}}}
{{{15 = 15}}}
OK