The alloy of copper and zinc contains 45% copper. how much copper should be added to this alloy so that it contains 60% copper.
Let us denote the weight of this alloy of copper and zinc through s.
In the wording of the condition for this task, it is reported that the copper content in this alloy is 45 percent, therefore, the weight of copper is (45/100) c = 0.45s, and the weight of zinc is c – 0.45s = 0.55s.
Let us denote by x the required mass of copper.
Then, after adding x kg of copper to this alloy, the weight of the alloy turned out to be c + x kg, and the weight of copper turned out to be equal to 0.45 c + x kg.
Since copper in the resulting alloy should be 60%, the following ratio should take place:
(0.45s + x) / (x + s) = 60/100.
We solve the resulting equation:
(0.45c + x) / (x + c) = 0.6;
0.45s + x = 0.6 * (x + s);
0.45s + x = 0.6x + 0.6s;
x – 0.6x = 0.6s – 0.45s;
0.4x = 0.15s;
x = 0.15s / 0.4;
x = 0.35s.
Answer: The weight of the added copper should be 35% of the weight of the original alloy.
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