Two pieces of chrome stone weigh 210g and 140g. The content of waste in the composition of each is 56%

Two pieces of chrome stone weigh 210g and 140g. The content of waste in the composition of each is 56% and 21%, respectively. If you put these two pieces together, what is the waste content of the resulting chrome stone?

1. Let:

m1 = 210 g – weight of the first chrome stone;
m2 = 140 g – weight of the second chrome stone;
p1 = 56% – waste content in the first stone;
p2 = 21% – waste content in the second stone;
m is the total weight of two stones;
p =? – the content of waste in them.
2. Let’s make equations for the amount of waste in stones and for the total weight:

p1m1 + p2m2 = pm; (one)
m1 + m2 = m. (2)
Dividing the equations, we find p:

p = (p1m1 + p2m2) / (m1 + m2);
p = (56 * 210 + 21 * 140) / (210 + 140) = (11 760 + 2 940) / 350 = 14700/35 = 42%.
Answer: 42%.