Question 83141
x = amount of 40% sugar solution needed
y = amount of 20% sugar solution needed
{{{.4x + .2y = .34*50}}}
This can be read as "Amount of sugar in 40% solution plus 
amount of sugar in 20% solution equals the sugar in the 34% solution"
{{{.4x + .2y = 17}}}
also
{{{x + y = 50}}}
multiply both sides of 1st equation by .4
{{{.4x + .4y = 20}}}
multiply both sides by -1
{{{-.4x - .2y = -17}}}
{{{ .4x + .4y = 20}}} add these together
{{{.2y = 3}}}
{{{y = 15}}}
{{{x + 15 = 50}}}
{{{X = 35}}}
So, there must be 35 ounces of the 40% solution and 15 ounces of the
20% solution to make 50 ounces of the 34% solution