Two alloys of which the first contains 40% nickel, and the second contains 60% nickel, were alloyed with each other

Two alloys of which the first contains 40% nickel, and the second contains 60% nickel, were alloyed with each other, receiving 200 kg of an alloy containing 55% nickel. how many kg was the mass of the first alloy?

The mass of the resulting alloy is 200 kg and it contains 55% nickel, that is:

200 * 55: 100 = 110 kg of nickel.

Let’s say that the first alloy weighed x kg, then the second alloy weighed 200 x kg.

Consequently, the first alloy contained:

x * 40: 100 = 0.4 * x kg of nickel,

and the second alloy contained:

(200 – x) * 60: 100 = 120 – 0.6 * x.

Thus, according to the condition of the problem, we can compose the following equation:

0.4 * x + 120 – 0.6 * x = 110,

0.2 * x = 10,

x = 10: 0.2,

x = 50 (kg).

Answer: 50 kg.