SOLUTION: A materials scientist has 6 lbs of a 40% silver alloy. How many pounds of pure silver must he mix with the entire 6 pounds of 40% alloy to obtain as much of a 62% alloy as he can?

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Question 266453: A materials scientist has 6 lbs of a 40% silver alloy. How many pounds of pure silver must he mix with the entire 6 pounds of 40% alloy to obtain as much of a 62% alloy as he can?
Found 2 solutions by josmiceli, drk:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
(pounds of silver in 62% alloy)/(total pounds of final alloy) = 62%
Let x = pounds of pure silver to be added
%28.4%2A6+%2B+x%29%2F%286+%2B+x%29+=+.62
%282.4+%2B+x%29%2F%286+%2B+x%29+=+.62
2.4+%2B+x+=+.62%2A%286+%2B+x%29
2.4+%2B+x+=+3.72+%2B+.62x
x+-+.62x+=+3.72+-+2.4
.38x+=+1.32
x+=+3.474
The scientist must add 3.474 pounds of silver
check:
%28.4%2A6+%2B+x%29%2F%286+%2B+x%29+=+.62
%28.4%2A6+%2B+3.474%29%2F%286+%2B+3.474%29+=+.62
5.874%2F9.474+=+.62
.620013+=+.62
close enough

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
This is a mixture problem. We can set up the following table.
alloy . . . . . % . . . . . LB . . . . . %lb
40% . . . . . .40 . . . . . . 6 . . . . .240
100% . . . . . 100 . . . . .x . . . . .100x
mixture . . . .62 . . . . .x + 6 . . 62x + 372
Looking at the third column we get
240 + 100x = 62x + 372
subtracting 62x we get
240 - 38x = 372
subtract 240 to get
132 = 38x
divide to get
x = 3.4736