Two substances: copper (density – 8900 kg / m3) and aluminum (density – 2700 kg / m3) were soldered into

Two substances: copper (density – 8900 kg / m3) and aluminum (density – 2700 kg / m3) were soldered into an alloy with a density of 6000 kg / m3. If copper was taken 10 kg, then determine the mass of aluminum and the mass of the substance obtained.

Let’s find the volume of copper:

V = m / p = 10/8900 = 1/890 m².

Let Mc – the mass of the alloy, Ma – the mass of aluminum, Vа – the volume of aluminum, then:

Ma / Vа = 2700 – the first equation of the system,

MS = 10 + Ma,

alloy volume = 1/890 + Vа,

then:

(10 + Ma) / (1/890 + Vа) = 6000 – the second equation of the system.

We get a system of equations. Having solved it, we get that Ms = 12.7 kg, Ma = 2.7 kg.

Answer: the mass of the alloy is 12.7 kg, the mass of aluminum is 2.7 kg.