SOLUTION: A copper alloy that is 35% copper is to be combined with an ally that is 75% copper. The result will be 750 kg of an alloy that is 60% copper. How many kg of each alloy should be

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Question 1144529: A copper alloy that is 35% copper is to be combined with an ally that is 75% copper. The result will be
750 kg of an alloy that is 60% copper. How many kg of each alloy should be used?

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
x of 75% copper
750-x of 35% copper


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Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!

Let x be the amount of the 75%  copper alloy needed (in kilograms), and

let y be the amount of the 35%  copper alloy needed.



The mass of the copper in the 75% alloy is 0.75x kilograms.

The mass of the copper in the 35% alloy is 0.35y kilograms.

The resulting alloy contains  0.75x + 0.35y kilograms of the copper and has the mass of 750 kilograms.


Thus you have these two equations


    x + y = 750    kilograms             (1)    (the total mass)

     = 0.60.                 (2)    (the resulting alloy concentration of copper)



From equation  (1), express  y = 750 - x.  Substitute it into equation (2) and multiply both sides of this equation by 750. 
You will get


    0.75*x + 0.35*(750-x) = 0.60*750.


From the last equation express x and calculate


    x =  = 468.75 kilograms of the 75% copper alloy are needed.


Then from equation (1),  y = 750 - 468.75 = 281.25 kilograms of the 35% copper alloy are needed.


Answer. 468.75 kilograms of the 75% alloy  and  281.25 kilograms of the 35% alloy are  needed.


Check.   = 0.6 = 60%.   ! Correct concentration !

The problem is just solved.
I used 2-equation setup and the Substitution method.

There are other solution methods, too.

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

There is entire bunch of introductory lessons covering various types of mixture problems
    - 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
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
in this site.

You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization,  from very detailed to very short.

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

The most relevant to your problem is 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 textbook in the section "Word problems" 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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