In an alloy of copper and zinc, containing 5 kg of zinc, 15 kg of zinc was added, after which the zinc content

| April 19, 2021 | education

In an alloy of copper and zinc, containing 5 kg of zinc, 15 kg of zinc was added, after which the zinc content in the alloy increased by 30%. What is the initial mass of the alloy if it is known that it contained more copper than zinc?

Let us denote the initial mass of the alloy for y kg. Then the zinc content will be 5 / y * 100%. After zinc was added, the mass of the new alloy became (y + 15) kg. Zinc will be 20 / (y + 15) * 100% in it. Since, according to the condition of the problem, the difference in the percentage of zinc was 30%, we obtain the equation:

20 / (y + 15) * 100 – 5 / y * 100 = 30,

2000 / (y + 15) – 500 / y = 30,

2000y – 500y – 7500 = 30y ^ 2 + 450y,

30y ^ 2 – 1050y + 7500 = 0,

y ^ 2 – 35y + 250 = 0,

D = b2 – 4ac,

D = 1225 – 1000 = 225.

y = (-b ± √D) / 2a

y = (35 ± 15) / 2

y1 = 25, y2 = 10.

According to the condition of the problem, there is less zinc, so only the first root is suitable.

Answer: originally the alloy had a mass of 25 kg.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.