Question 147291
Let {{{x}}}= gallons of 50% antifreeze to be added
How much antifreeze is in it?
{{{.5x}}} gallons
How much antifreeze is in the 20% solution?
{{{.2*80 = 16}}} gallons
What,s the total amount of solution you end up with?
{{{x + 80}}}
In words:
(amount of antifreeze) / (total amount of solution) = % antifreeze
{{{(.5x + 16) / (x + 80) = .4}}}
multiply both sides by {{{x + 80}}}
{{{.5x + 16 = .4*(x + 80)}}}
{{{.5x + 16 = .4x + 32}}}
{{{.1x = 16}}}
{{{x = 160}}}
160 gallons of the 50% antifreeze must be added
check answer:
{{{(.5x + 16) / (x + 80) = .4}}}
{{{(.5*160 + 16) / (160 + 80) = .4}}}
{{{(80 + 16) / 240 = .4}}}
{{{96 / 240 = .4}}}
{{{96 = .4*240}}}
{{{96 = 96}}}
OK