SOLUTION: A metal recycling plant has some scrap metal that is 41% copper. It also has some other scrap metal that is 5% copper. The scrap metal is melted together and produces 1700 g of met
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Question 1101216: A metal recycling plant has some scrap metal that is 41% copper. It also has some other scrap metal that is 5% copper. The scrap metal is melted together and produces 1700 g of metal that is 44% copper. How many grams of the 51% copper metal were mixed with the 41% copper metal?
A.1190 g
B.510 g
C.867 g
D.1700 g Found 2 solutions by richwmiller, greenestamps:Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website! We know the total amount is 1700 g
We know the percentage of the total amount is 44%
We know the total amount has 748 g of 100%
We want to know the amount of copper at 41%
We want to know the amount of copper at 51%
x+y=1700,
0.41*x+0.51*y=0.44*1700
0.41*x+0.51*y=748
x=1700-y
0.41*(1700-y)+0.51*y=748
697-0.41y+0.51*y=748
0.1*y=51
We now know amount of copper at 51%
y=510 g at 51%
x=1700-y
We now know amount of copper at 41%
x=1190 g at 41%
check
0.41*1190+0.51*510=0.44*1700
487.9+260.1=748
748=748
ok
You can solve mixture problems like this quickly using the method of alligation.
Do a search of the internet if you want to learn about the method; I will just give you a quick description of how your example is solved using the method.
The percentages of copper in the two ingredients in the mixture are 41 and 51; the percentage in the mixture is 44.
The 44 is 3/10 of the way from 41 to 51 (from 41 to 51 is 10; from 41 to 44 is 3).
That means 3/10 of the mixture is the 51% copper scrap metal.
