SOLUTION: A jeweler has four rings, each weighing 20 grams, made of an alloy of 5% silver and 95% gold. He decides to melt down the rings and add enough silver to reduce the gold content to

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Question 584614: A jeweler has four rings, each weighing 20 grams, made of an alloy of 5% silver and 95% 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.)
G(x) =

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A jeweler has four rings, each weighing 20 grams, made of an alloy of 5% silver and 95% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 80%.
:
Total weight of the 4 rings 80 grams
:
Let x = amt of extra silver required
:
A mixture of gold equation (the amt of gold remains the same only the % changes)
.95(80) = .80(x+80)
76 = .80x + 64
76 - 64 = .8x
12 = .8x
x = 12/.8
x = 15 grams of silver required to reduce 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.)
G(x) =
:
In the original mixture of 80 gram, 76 grams is pure gold, therefore
G(x) = 76%2F%28%28x%2B80%29%29
Check this by adding 15 grams of silver like we did above
G(x) = 76%2F%28%2815%2B80%29%29
G(x) = .8 or 8/10 is pure gold