SOLUTION: How many pounds of a 12% aluminum alloy must be mixed with 400 pounds of a 25% aluminum alloy to make a 17% aluminum alloy?

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Question 126875: How many pounds of a 12% aluminum alloy must be mixed with 400 pounds of a 25% aluminum alloy to make a 17% aluminum alloy?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
(pounds of aluminum in 12% alloy) + (pounds of aluminum in 25% alloy)
divided by (total pounds of mixture) = 17%
Let a = pounds of 12% alloy needed
Let b = pounds of 25% alloy needed
%28.12a+%2B+.25b%29+%2F+%28a+%2B+b%29+=+.17
b+=+400
%28.12a+%2B+.25%2A400%29+%2F+%28a+%2B+400%29+=+.17
%28.12a+%2B+100%29+%2F+%28a+%2B+400%29+=+.17
.12a+%2B+100+=+.17%28a+%2B+400%29
.12a+%2B+100+=+.17a+%2B+68
.05a+=+32
a+=+640
640 pounds of 12% alloy must be used
check answer
%28.12a+%2B+.25b%29+%2F+%28a+%2B+b%29+=+.17
%28.12%2A640+%2B+.25%2A400%29+%2F+1040+=+.17
%2876.8+%2B+100%29+%2F+1040+=+.17
176.8+=+1040%2A.17
176.8+=+176.8
OK