SOLUTION: a silversmith has two alloys. the first alloy is 18% silver and the second is 54% silver. how many grams of each should be mixed to produce 120 grams of an alloy that is 39% silver

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Question 64809: a silversmith has two alloys. the first alloy is 18% silver and the second is 54% silver. how many grams of each should be mixed to produce 120 grams of an alloy that is 39% silver?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of 18% silver
Then 120-x=amount of 54% silver
Now we know that the amount of pure silver in the 18% mixture (.18)(x) plus the amount of pure silver in the 54% mixture (120-x)(.54) must equal the amount of pure silver in the final mixture (120)(.39) so our equation to solve is:

.18x+.54(120-x)=(120)(.39) simplifying we get:
.18x-.54x+64.8=46.8 collecting like terms we have:
-.36x=-64.8+46.8=-18
x=50 grams of 18% silver
and 120-x=120-50 =70 grams of 54% silver
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70(.54)+50(.18)=120(.39)
37.8+9=46.8
46.8=46.8
Hope this helps. Happy holidays.----ptaylor