What mass of copper (P1 = 8900 kg / m3) and zinc (P2 = 7100 kg / m3) should be taken to obtain

What mass of copper (P1 = 8900 kg / m3) and zinc (P2 = 7100 kg / m3) should be taken to obtain the mass of brass equal to m = 5 kg (P = 8400 kg / m3)

1) m1 + m2 = m3, where m1 is the mass of copper (x), m2 is the mass of zinc (y), m3 is the mass of brass (m3 = 5 kg).

x + y = 5; x = 5 – y.

2) V1 + V2 = V3, where V1 is the volume of copper (V1 = m1 / ρ1, where ρ1 = 8900 kg / m3), is the volume of zinc (V2 = m2 / ρ2, where ρ2 = 7100 kg / m3), V3 is volume of brass (V3 = m3 / ρ3, where ρ3 = 8400 kg / m3).

x / 8900 + y / 7100 = 5/8400.

(5 – y) / 8900 + y / 7100 = 5/8400 | * 8900 * 7100.

(5 – y) * 7100 + 8900y = 37613.

35500 – 7100y + 8900y = 37613.

y = 1.17 kg.

x = 5 – 1.17 = 3.83 kg.