SOLUTION: A metal alloy is 25% copper. Another metal alloy is 50% copper. How many grams of the 50% copper alloy should be used to make 1000 grams of a metal alloy that is 45% copper ?

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Question 1025203: A metal alloy is 25% copper. Another metal alloy is 50% copper. How many grams of the 50% copper alloy should be used to make 1000 grams of a metal alloy that is 45% copper ?
Answer by mathmate(429) About Me  (Show Source):
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Question:
A metal alloy is 25% copper. Another metal alloy is 50% copper. How many grams of the 50% copper alloy should be used to make 1000 grams of a metal alloy that is 45% copper ?

Solution:
The key to answering mixture problems is to calculate the weight of the pure components.
We know the total is 1000 grams, and 50% means 450 grams of pure copper.
Let x=weight of the 50% alloy, then
(1000-x)=weight of the 25% alloy.
Total weight of pure copper
=x(0.50)+(1000-x)(0.25) g
Since we know this weight must be 500 grams, so we equate and solve for x.
x(0.50)+(1000-x)(0.25) = 500
0.5x-0.25x+250=450
0.25x=450-250=200
means
x=200/0.25=800
Answer: 800 grams of the 50% copper alloy will be needed
(hence (1000-800)=200 grams of the 25% alloy.