SOLUTION: How many grams of gold must be added to 500 grams of alloy containing 30% gold and 70% silver to obtain 40% gold and 60% silver?

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Question 1022164: How many grams of gold must be added to 500 grams of alloy containing 30% gold and 70% silver to obtain 40% gold and 60% silver?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = grams of gold to be added
+.3%2A500+=+150+ grams of gold in 30% alloy
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+%28+x+%2B+150+%29+%2F+%28+x+%2B+500+%29+=+.4+
+x+%2B+150+=+.4%2A%28+x+%2B+500+%29+
+x+%2B+150+=+.4x+%2B200+
+.6x+=+50+
+x+=+83.333+
83 and 1/3 grams of gold must be added
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check:
+%28+x+%2B+150+%29+%2F+%28+x+%2B+500+%29+=+.4+
+%28+83.333+%2B+150+%29+%2F+%28+83.333+%2B+500+%29+=+.4+
+233.333+%2F+583.333+=+.4+
+.3999997+=+.4+
error due to rounding off
OK