SOLUTION: A jeweler has five rings, each weighing 16 grams, made of an alloy of 10% silver and 90% gold. He decides to melt down the rings and add enough silver to reduce the gold content to

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Question 914456: A jeweler has five rings, each weighing 16 grams, made of an alloy of 10% silver and 90% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 80%.
(a) Construct a model that gives the fraction G(x) of the new alloy that is pure gold. (Let x represent the number of grams of silver added.)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5 rings, 16 grams each ----> 5*16 = 80 grams total

10% silver: 80*0.10 = 8 grams of pure silver
90% gold: 80*0.90 = 72 grams of pure gold

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We have 72 grams of pure gold out of 80 grams of alloy (silver + gold)

Currently, the fraction is 72/80. This leads to 9/10 = 90% gold

Now add x grams of pure silver. We do NOT add this to the 72 since that represents all gold. We add this to the 80 since that represents silver+gold.


So we have this fraction now: 72%2F%2880%2Bx%29

So the model is G%28x%29+=+72%2F%2880%2Bx%29

We want the gold fraction to be equal to 80/100 (ie 80%), so g%28x%29+=+80%2F100 and 72%2F%2880%2Bx%29+=+80%2F100



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Solve for x

72%2F%2880%2Bx%29+=+80%2F100

72%2F%2880%2Bx%29+=+4%2F5

72%2A5+=+4%2880%2Bx%29

360+=+320%2B4x

360+-+320=4x

40=4x

40%2F4=x

10=x

x=10

You need to add 10 grams of pure silver to get an 80% gold alloy.


Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
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Thanks,

Jim