Two alloys of which the first contains 10% copper and the second contains 30% copper, were fused

Two alloys of which the first contains 10% copper and the second contains 30% copper, were fused with each other, obtaining an alloy containing 25% copper. Determine how many kilograms the mass of the resulting alloy will be, if it is known that the mass of the second alloy was more than the mass of the first by 70 kg

Let X kg be the mass of the first alloy, then the mass of the second alloy X + 70.

To find the mass of copper contained in the alloy, you need to multiply the mass of the alloy by the percentage of copper in this alloy:

The mass of copper in the first alloy is 0.1x

The mass of copper in the second alloy is 0.3 * (x + 70).

Find the mass of the third alloy by adding the masses of the first and second – x + x + 70 = 2x + 70.

Let’s find the mass of copper contained in the third alloy – 0.1x + 0.3 * (x + 70).

Let’s make the equation:

(2x + 70) * 0.25 = 0.1x + 0.3 * (x + 70)

0.5x + 17.5 = 0.1x + 0.3x + 21

0.5x – 0.1x – 0.3x = 21 – 17.5

0.1x = 3.5

x = 35 kg is the mass of the first alloy.

Let’s find the mass of the second alloy (it is 70 kg more).

35 + 70 = 105 kg – the mass of the second alloy.

Let’s find the mass of the third alloy:

35 + 105 = 140 kg is the mass of the third alloy.

Answer: 140 kg