SOLUTION: How many grams of pure silver must a silversmith mix with a 45% silver alloy to produce 200 grams of a 50% alloy?

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Question 124249This question is from textbook college algebra
: How many grams of pure silver must a silversmith mix with a 45% silver alloy to produce 200 grams of a 50% alloy? This question is from textbook college algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
How many grams of pure silver must a silversmith mix with a 45% silver alloy to produce 200 grams of a 50% alloy?
:
Let x = amt of pure silver required to produce 200 gr of 50% alloy
:
Then (200-x) = amt of 45 % silver required
:
Write a percent silver equation:
:
.45(200-x) + 1.0x = .50(200)
:
90 -.45x + 1.0x = 100
:
-.45x + 1.0x = 100 - 90
:
.55x = 10
x = 10%2F.55
x = 18.2 grams of pure silver required
:
:
Check solution:
200 - 18.2 = 181.8 gr of 45 % alloy required
:
.45(181.8) + 18.2 = .5(200)
81.8 + 18.2 = 100; confirms our solution of x = 18.2 grams