There are two alloys available. The first contains 10% nickel and the second 25% nickel. From these two alloys, a third 150

There are two alloys available. The first contains 10% nickel and the second 25% nickel. From these two alloys, a third 150 kg alloy containing 20% nickel was obtained. How many kilograms is the mass of the first alloy less than the mass of the second?

According to the condition of the problem, the resulting alloy weighing 150 kg contains 20% nickel, which means that the mass of nickel in it is equal to:

150: 100 * 20 = 30 kg.

Suppose that to obtain this solution, we took x kg of 25% alloy, which means that the mass of 10% alloy is 150 – x kg.

Let’s compose and solve the equation:

0.25 * x + 0.1 * (150 – x) = 30,

0.25 * x + 15 – 0.1 * x = 30,

0.15 * x = 15,

x = 15: 0.15,

x = 100 (kg) is the mass of the second alloy.

150 – 100 = 50 (kg) – the mass of the first alloy.

100 – 50 = 50 (kg) – the mass of the first alloy is 50 kg less than the mass of the second.