SOLUTION: A metallurgist has one alloy containing 40% aluminum and another contained 57% aluminum. How many pounds of each alloy must he use to make 54 pounds containing 51% aluminum.

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Question 295319: A metallurgist has one alloy containing 40% aluminum and another contained 57% aluminum. How many pounds of each alloy must he use to make 54 pounds containing 51% aluminum.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the number of pounds of 40% aluminum, B be the number of pounds of 57% aluminum.
1.A%2BB=54
2.40A%2B57%2AB=51%2854%29=2754
Use eq. 1,
A%2BB=54
A=54-B
Substitue into eq. 2,
40%2854-B%29%2B57B=2754
2160-40B%2B57B=2754
17B=594
B=594%2F17
Then from eq.1,
A=54-B=54-594%2F17
A=918%2F17-594%2F17
A=324%2F17
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Use 324%2F17(or about 19.1 lbs) of 40% alloy and 594%2F17(or about 34.9 lbs) of 57% alloy to get 54 lbs of 51% aluminum.