SOLUTION: How much of an alloy that is 20% copper should be mixed with 600 ounces of an alloy that is 60% copper in order to get an alloy that is 30% ​copper?

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Question 1133341: How much of an alloy that is 20% copper should be mixed with 600 ounces of an alloy that is 60% copper in order to get an alloy that is 30% ​copper?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The traditional algebraic solution method....

20% of x ounces, plus 60% of 600 ounces, equals 30% of (x+600) ounces.



The equation is easily solved with basic algebra.

I leave that to you....

A faster path to the solution of any mixture problem like this involving two ingredients....

30% is 1/4 of the way from 20% to 60%. (The distance from 20% to 60% is 40%; the distance from 20% to 30% is 10%; 10% is 1/4 of 40%.)

That means 1/4 of the alloy must be the higher percentage.

The 600 ounces of 60% copper are 1/4 of the total, so the total is 600*4 = 2400 ounces; that means 1800 ounces of the 20% alloy.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
Let  "x" be the amount of the 20% copper alloy, in ounces (the value under the question.


Then the balance equation for the copper content is


    0.2x + 0.6*600 = 0.3*(x+600)


saying that the copper content in the final alloy is the sum of the copper content in each of the two ingredients.


Simplify and solve for x


    x =  = 1800.


Answer.  1800 ounces of the 20% copper alloy.


CHECK.   1800*0.2 + 600*0.6 = 720 ounces of the copper, exactly as 

         0.3*(600+1800) = 720 ounces of the copper.   ! Correct !

Solved.

------------------

It is a standard and typical mixture word problem.

See introductory lessons
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for alloys  (*)
    - Typical word problems on mixtures from the archive
in this site.

Read them and become an expert in solution the mixture word problems.

Regarding alloys,  you have the lesson marked  (*)  in the list.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Mixture problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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