SOLUTION: A metallurgist has an alloy with 15​% titanium and an alloy with 25​% titanium. He needs 100 grams of an alloy with 21​% titanium. How much of each alloy should be mixed to a

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Question 1135611: A metallurgist has an alloy with 15​% titanium and an alloy with 25​% titanium. He needs 100 grams of an alloy with 21​% titanium. How much of each alloy should be mixed to attain the 100 grams of alloy with 21​% ​titanium?
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
x = grams of 15% titanium
y = grams of 25% titanium

Make two equations:
x+%2B+y+=+100
0.15x+%2B+0.25y+=+0.21%28100%29

Simplify second equation:
x+%2B+y+=+100
0.15x+%2B+0.25y+=+21

Multiply second equation by -4:
x+%2B+y+=+100
-0.6x+-+y+=+-84

Add the equations together:
0.4x+=+16

Solve for x:
x+=+40

x = 40, so that means the metallurgist uses 40 grams of the 15% titanium. Since x + y = 100 (from our first equation), that means the metallurgist uses 60 grams of the 25% titanium.