Question 1197547
.
How many kilograms of nickel silver containing 15% zinc and how many kilograms 
of nickel silver containing 33% zinc must be melted together to produce 748 kg 
of a new nickel silver containing 28% zinc?
~~~~~~~~~~~~~~


<pre>
I take x kilograms of the 33% zink alloy
and (748-x) kilograms of the 15% zink alloy.


For any x in between of 0 and 748 kg, the total mass of 748 kg alloy will be provided, correct ?


Hence, I only need to provide necessary concentration of 28% zink in the final mixture.


For it, I write an equation for the pure zink masses in components and in the final mixture

    0.15*(748-x) + 0.33x = 0.28*748 kilograms  for the mass of the pure zink.      (1)


The setup is done, and if you do understand it, you are great !


Now I will solve the equation to find x.

You should simplify it in couple of simple steps


    0.15*748 - 0.15x + 0.33x = 0.28*748

                    0.18x    = 0.28*748 - 0.15*748

                    0.18x    =      97.24

                        x    =      97.24/0.18 = 540.222 kilograms.


<U>ANSWER</U>.  540.222 kg of the 33% zinc alloy should be mixed with 748-540.222 = 207.778 kg of the 15% zinc alloy.


<U>CHECK</U>.  Mass of the pure zink in components, in total = 0.33*540.222 + 0.15*207.778 = 209.44 kg.

        Mass of the zink in the final mixture is  0.28*748 = 209.44 kg.

        We obtain the same mass in both sides of the equation (1), which means that the answer and the solution both are correct.
</pre>

Solved.


Now accept my congratulations, since from now you know how to solve mixture problems.