SOLUTION: A silversmith has two alloys, one containing 70% silver and the other 40% silver. How much of each should be melted and combined to obtain 400 grams of an alloy containing 61% silv

Question 526733: A silversmith has two alloys, one containing 70% silver and the other 40% silver. How much of each should be melted and combined to obtain 400 grams of an alloy containing 61% silver?
______40% alloy
___ g 70% alloy
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Alloy one
=========
Amount = x grams
Silver = 70% = 0.7
Alloy two
=========
Amount = 400-x grams
Silver = 40% = 0.4
Mixture Alloy
============
Amount = 400 grams
Silver = 61% = 0.61

(Amount of Alloy one)*sliver + (Amount of Alloy two)*sliver = (Amount of Mixture Alloy)*sliver
(x)(0.7)+(400-x)(0.4)=400*0.61
0.7x+160-0.4x=244
0.7x-0.4x=244-160
0.3x=84
0.3x/0.3=84/0.3
x=280

Alloy one
=========
Amount = x = 280 grams
Silver = 70% = 0.7
Alloy two
=========
Amount = 400-x - 400-280 = 120 grams
Silver = 40% = 0.4
Mixture Alloy
============
Amount = 400 grams
Silver = 61% = 0.61

120grams ______40% alloy
280grams___ g 70% alloy
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