To an alloy of copper and zinc containing 10 kg of copper, 20 kg of zinc was added, as a result, the copper content in the alloy decreased by 25%, which was the initial mass of the alloy.
Let the initial mass of the alloy be x kg, from the condition it is known that the copper in the alloy was 10 kilograms, then it turns out that the zinc in the alloy was (X – 10) kilograms.
Let’s find how much of the alloy is the mass of copper:
10 / x 100% = 1000 / x%;
Then 20 kilograms of zinc was added to the alloy, then the new mass of the alloy is: (x + 20) kg, and the copper in the alloy is still 10 kilograms.
find the copper content in the new alloy:
10 / (x + 20) 100% = 1000 / (x + 20)%;
It is known that when 20 kilograms of zinc was added to the alloy, the copper content of the alloy decreased by 25% compared to the original alloy.
Let’s make the equation:
1000 / X – 1000 / (X + 20) = 25;
1000 * (X + 20) – 1000X = 25X * (X + 20);
1000X + 20,000 – 1000X = 25X ^ 2 + 500X;
20,000 – 25X ^ 2 – 5000X = 0;
25X ^ 2 + 5000X – 20,000 = 0;
X ^ 2 + 20X + 800 = 0;
D = 400 + 4 800 = 3600;
x1 = (-20 – 60) / 2 <0, does not satisfy the condition of the problem;
x2 = (-20 + 60) / 2 = 20.
Answer: 20 kilograms is the initial mass of the alloy.
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