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

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 !