SOLUTION: A metal worker has a metal alloy that is 30% copper and another alloy that is 80% copper. How many kilograms of each alloy should the metalworker combine to creat 60 kilograms of a

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Question 971955: A metal worker has a metal alloy that is 30% copper and another alloy that is 80% copper. How many kilograms of each alloy should the metalworker combine to creat 60 kilograms of a 51% copper alloy?
Found 4 solutions by lwsshak3, ikleyn, josgarithmetic, greenestamps:
Answer by lwsshak3(11628) About Me  (Show Source):
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A metal worker has a metal alloy that is 30% copper and another alloy that is 80% copper. How many kilograms of each alloy should the metalworker combine to creat 60 kilograms of a 51% copper alloy?
let x=amt of 30% copper alloy to combine
60-x=amt of 80% copper alloy to combine
..
30%x+80%(60-x)=51%*60
.30x+40-.80x=30.6
.50x=9.4
x=50.6
How many kilograms of each alloy should the metalworker combine?
30% copper alloy: 9.4 kg
80% copper alloy: 50.6 kg

Answer by ikleyn(53875) About Me  (Show Source):
You can put this solution on YOUR website!
.
A metal worker has a metal alloy that is 30% copper and another alloy that is 80% copper.
How many kilograms of each alloy should the metalworker combine to create 60 kilograms of a 51% copper alloy?
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        The solution and the answer in the post by @lwsshak3 are incorrect due to arithmetic error.
        See my correct solution below.


let x=amt of 30% copper alloy to combine
60-x=amt of 80% copper alloy to combine
..
0.3x + 0.8*(60-x) = 0.51*60
0.3x + 48 - 0.8x = 30.6
48 - 30.6 = 0.8x - 0.3x
0.50x = 17.4
x = 34.8
How many kilograms of each alloy should the metalworker combine?
30% copper alloy: 34.8 kg
80% copper alloy: 60-34.8 = 25.2 kg

CHECK  for the final concentration   %280.3%2A34.8%2B0.8%2A25.2%29%2F%2834.8%2B25.2%29 = 0.51.         ! precisely correct !

Solved.



Answer by josgarithmetic(39823) About Me  (Show Source):
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ALLOY         PERCENT         QUANTITY           PURE
 'an'           30              60-x             30(60-x)
 'another       80               x               80x
Blend           51              60               51*60

30%2860-x%29%2B80x=51%2A60. Solve this for x.

30%2A60-30x%2B80x=51%2A60
80x-30x=51%2A60-30%2A60
%2880-30%29x=60%2851-30%29
x=60%28%2851-30%29%2F%2880-30%29%29
x=60%2821%2F50%29
x=6%2A21%2F5
highlight%28x=25.2%29 of the "another" or 80% copper alloy and
highlight%2834.8%29 of the 30% copper alloy.

Answer by greenestamps(13355) About Me  (Show Source):
You can put this solution on YOUR website!


Two other tutors have provided essentially identical solutions using the standard formal algebraic method for solving 2-part mixture problems like this.

Here is a solution using a less formal method that can be used to solve any problem like this. The method can be especially fast and easy, especially if the numbers in the problem are "nice".

(1) Use a number line if it helps to observe/calculate that 51% is 21/50 of the way from 30% to 80%.
(2) That means 21/50 of the mixture should be the alloy that is 80% copper.

21/50 of 60 kg is (.42)(60) = 25.2 kg.

ANSWER: 25.2 kg of the 80% copper alloy and (60-25.2)=34.8 kg of the 30% copper alloy.