SOLUTION: A silversmith has two alloys, one containing 35% silver and the other 66% silver. How much of each should be melted and combined to obtain 100 grams of an alloy containing 45% silv

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A silversmith has two alloys, one containing 35% silver and the other 66% silver. How much of each should be melted and combined to obtain 100 grams of an alloy containing 45% silv      Log On


   

Question 344455: A silversmith has two alloys, one containing 35% silver and the other 66% silver. How much of each should be melted and combined to obtain 100 grams of an alloy containing 45% silver?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the amount of 35% silver alloy, B the amount of 66% silver alloy.
Total weight equation:
1.A%2BB=100
Total silver concentration equation:
35A%2B66B=45%28100%29
2.35A%2B66B=4500
From eq. 1,
A=100-B
Substitute in eq. 2,
35%28100-B%29%2B66B=4500
3500-35B%2B66B=4500
31B=1000
highlight%28B=1000%2F31%29grams
.
.
.
Then from eq. 1,
A%2B1000%2F31=100
A=3100%2F31-1000%2F31
highlight%28A=2100%2F31%29grams