Question 1107466: A metal recycling plant has some scrap metal that is 45% copper. It also has some other scrap metal that is 25% copper. The scrap metal is melted together to produce 1530 g of metal that is 29% copper. How many grams of the 25% copper metal were mixed with the 45% copper metal?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x is the number of grams of 45% copper.
y is the number of grams of 25% copper.
these are melted together to produce 1530 grams of 29% copper.
you get x + y = 1530
you get .45 * x + .25 * y = .29 * 1530.
these two equations need to be solved simultaneously.
leave the first equation as is and multiply both sides of the second equation by 4 to get:
x + y = 1530
1.8 * x + y = 4 * .29 * 1530
simplify the second equation and leave the first equation as is to get:
x + y = 1530
1.8 * x + y = 1774.8
subtract the first equation from the second to get:
.8 * x = 244.8
solve for x to get x = 244.8 /.8 = 306
since x + y = 1530, and x = 306, solve for y to get y = 1530 - 306 = 1224.
it appears that 306 grams of 45% copper and 1224 grams of 25% copper are combined to make 1530 grams of 29% copper.
to confirm this is true, replace x and y in the original equations to see if they are true.
the original equations are:
x + y = 1530
.45 * x + .25 * y = .29 * 1530
replacing x and y with their respective values gets you:
306 + 1224 = 1530 becomes 1530 = 1530 which is true.
.45 * 306 + .25 * 1224 = .29 * 1530
simplify to get 137.7 + 306 = 443.7
simplify further to get 443.7 = 443.7 which is true.
both original equations are true when you replace x with 306 and y with 1224.
this confirms the solution is correct.
the solution is that 1224 grams of 25% copper were mixed with the 45% copper metal.
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