Question 266453
In words:
(pounds of silver in 62% alloy)/(total pounds of final alloy) = 62%
Let {{{x}}} = pounds of pure silver to be added
{{{(.4*6 + x)/(6 + x) = .62}}}
{{{(2.4 + x)/(6 + x) = .62}}}
{{{2.4 + x = .62*(6 + x)}}}
{{{2.4 + x = 3.72 + .62x}}}
{{{x - .62x = 3.72 - 2.4}}}
{{{.38x = 1.32}}}
{{{x = 3.474}}}
The scientist must add 3.474 pounds of silver 
check:
{{{(.4*6 + x)/(6 + x) = .62}}}
{{{(.4*6 + 3.474)/(6 + 3.474) = .62}}}
{{{5.874/9.474 = .62}}}
{{{.620013 = .62}}}
close enough