There are two alloys, the masses of which differ by 54 kilograms. The first alloy contains 10% tin, the second 30% tin.

There are two alloys, the masses of which differ by 54 kilograms. The first alloy contains 10% tin, the second 30% tin. From these two alloys, a third alloy was obtained, which contains 18.2% tin. Find the mass of the lighter alloy.

We introduce the variable x and denote the mass of the first alloy as such, the mass of the second alloy will be (x – 54). Find how much tin is in each alloy:
x * 10% = 0.1x – in the first alloy;
(x – 54) * 30% = 0.3x – 16.2 – in the second alloy.
According to the condition, the third tin alloy contains 18.2%, we make the equation:
0.1x + 0.3x – 16.2 = 0.182 * (x + x – 54)
0.4x – 16.2 = 0.364x – 9.828
0.036x = 6.372
x = 177 (kg) is the mass of the first alloy;
177 – 54 = 123 (kg) – the mass of the second alloy.
Answer: 123 kg is the weight of the lighter alloy.