A piece of lead and tin alloy has a density of 8.3 g / cm3. Determine the mass of lead in the alloy

A piece of lead and tin alloy has a density of 8.3 g / cm3. Determine the mass of lead in the alloy if the mass of the piece is 664 g.

Given:

ro = 8.3 g / cm ^ 3 – density of the alloy of tin and lead;

m = 664 grams – mass of a piece of tin and lead alloy;

ro1 = 11.3 g / cm ^ 3 is the density of lead;

ro2 = 7.3 g / cm ^ 3 is the density of tin.

It is required to find the mass of lead m1.

V = m / ro is the volume of the alloy piece;

V = V1 + V2 = m1 / ro1 + m2 / ro2 = m1 / ro1 + (m – m1) / ro2;

m1 / ro1 + (m – m1) / ro2 = m / ro;

(m1 * ro2 + m * ro1 – m1 * ro1) / (ro1 * ro2) = m / ro;

m1 * ro2 + m * ro1 – m1 * ro1 = m * ro1 * ro2 / ro;

m1 * (ro2 – ro1) + m * ro1 = m * ro1 * ro2 / ro;

m1 * (ro2 – ro1) = m * ro1 * ro2 / ro – m * ro1;

m1 * (ro2 – ro1) = (m * ro1 * ro2 – m * ro1 * ro) / ro = m * ro1 * (ro2 – ro) / ro;

m1 = (m * ro1 * (ro2 – ro)) / (ro * (ro2 – ro1)) = (664 * 11.3 * (7.3 – 8.3)) / (8.3 * (7, 3 – 11.3)) = -7503.2 / -33.2 = 226 grams.

Answer: The mass of lead is 226 grams.