Question

В сплаве олова и меди содержалось 11 кг меди. После того как в сплав добавили 7,5 кг олова, концентрация олова повысилась на 33%. Какова первоначальная масса сплава?

Answer 1

Пусть  (кг) первоначальная масса сплава, тогда:
(кг) масса 1% первоначального сплава;

Answer 2

Calculation of the Initial Mass of the Alloy

To calculate the initial mass of the alloy, we can use the information provided. We know that initially, the alloy contained 11 kg of copper. After adding 7.5 kg of tin to the alloy, the concentration of tin increased by 33%.

Let's denote the initial mass of the alloy as x kg. The concentration of tin in the alloy can be calculated using the formula:

Concentration of Tin = Mass of Tin / Total Mass of Alloy

Initially, the concentration of tin in the alloy is:

11 kg / x kg

After adding 7.5 kg of tin, the concentration of tin increases by 33%. This means the new concentration of tin is:

1.33 * (11 kg / x kg)

We can set up the equation:

1.33 * (11 kg / x kg) = (11 kg + 7.5 kg) / (x kg + 7.5 kg)

Simplifying the equation, we get:

1.33 * (11 / x) = (11 + 7.5) / (x + 7.5)

To solve for x, we can cross-multiply:

1.33 * (11 + 7.5) * x = 11 * (x + 7.5)

Simplifying further:

1.33 * 18.5 * x = 11x + 11 * 7.5

24.405x = 11x + 82.5

**24.405