Question 164971This question is from textbook
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An alloy of metals is 25% copper. ANother alloy is 50% copper. how much of each alloy should be used to make 1000 grams of an alloy that is 45% copper?
This question is from textbook
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! An alloy of metals is 25% copper. Another alloy is 50% copper. how much of each alloy should be used to make 1000 grams of an alloy that is 45% copper?
We have a system of equation in two variables.
Let x = alloy of metal
Let y = Another alloy
THEN:
x + y = 1000...Equation A
The question tells us that 25% is copper and that the other alloy is 50% copper.
From this information we make our second equation.
0.25x + 0.50x = 0.45 (1000)...Equation B
Here is your system of equations:
x + y = 1000...Equation A
0.25x + 0.50y = 0.45 (1000)...Equation B
I will solve for y in Equation A. Of course, you can solve for x or y (your choice).
From this system of equations, it is easier playing with equation A.
x + y = 1000...Equation A
Solving for x, I get:
x = 1000 - y
I will now plug x = 1000 - y into Equation B to find the value of y.
0.25x + 0.50y = 0.45 times (1000)
0.25(1000 - y) + 0.50y = 450
250 - 0.25y + 0.50y = 450
250 + 0.25y = 450
0.25y = 450 - 250
0.25y = 200
y = 200/0.25
y = 800
We just found the value of y to be 800.
To find x, we plug y = 800 for y in EITHER Equation A or Equation B.
I will select the easy Equation A.
x + y = 1000...Equation A
x + 800 = 1000
Solving for x, I get:
x = 1000 - 800
x = 200
Finals answer: 200 alloy of metal should be used and 800 of the other alloy should be used.
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