SOLUTION: How many grams of pure gold must be mixed with 40% gold alloy to produce 100 grams of 52% alloy?

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Question 994496: How many grams of pure gold must be mixed with 40% gold alloy to produce 100 grams of 52% alloy?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = grams of pure gold needed
+.4%2A%28+100+-+x+%29+ = grams of gold in 40% alloy
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+%28+x+%2B+.4%2A%28+100+-+x+%29+%29+%2F+100+=+.52+
+x+%2B+40+-+.4x+=+.52%2A100+
+.6x+%2B+40+=+52+
+.6x+=+12+
+x+=+20+
20 grams of pure gold are needed
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check:
+%28+x+%2B+.4%2A%28+100+-+x+%29+%29+%2F+100+=+.52+
+%28+20+%2B+.4%2A%28+100+-+20+%29+%29+%2F+100+=+.52+
+%28+20+%2B+.4%2A80+%29+%2F+100+=+.52+
+52+=+.52%2A100+
+52+=+52+
OK