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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?
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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.
ANSWER. 540.222 kg of the 33% zinc alloy should be mixed with 748-540.222 = 207.778 kg of the 15% zinc alloy.
CHECK. 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.
Solved.
Now accept my congratulations, since from now you know how to solve mixture problems.