SOLUTION: how many g of gold should coin of 38% gold be if when combined with 3 g of pure gold, it forms a metal that is 78% gold

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Question 1005947: how many g of gold should coin of 38% gold be if when combined with 3 g of pure gold, it forms a metal that is 78% gold
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = grams of 38% gold needed
+.38x+ = grams of gold in 38% gold
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+%28+.38x+%2B+3+%29+%2F+%28+x+%2B+3+%29+=+.78+
+.38x+%2B+3+=+.78%2A%28+x+%2B+3+%29+
+.38x+%2B+3+=+.78x+%2B+2.34+
+.4x+=+.66+
+x+=+1.65+
1.65 grams of 38% gold are needed
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check:
+%28+.38x+%2B+3+%29+%2F+%28+x+%2B+3+%29+=+.78+
+%28+.38%2A1.65+%2B+3+%29+%2F+%28+1.65+%2B+3+%29+=+.78+
+%28+.627+%2B+3+%29+%2F+4.65+=+.78+
+3.627+=+3.627+
OK