# From 160 tons of cast iron with a mass fraction of carbon 6%, you can get steel with a mass

From 160 tons of cast iron with a mass fraction of carbon 6%, you can get steel with a mass fraction of carbon 1.5%, the mass of which is equal to?

w (C) = m (C) / m (cast iron)

First, let’s calculate the mass of carbon in cast iron:

m (C) = w (C) * m (cast iron) = 0.06 * 160 = 9.6 t

m (Fe) = m (cast iron) – m (C) = 160 – 9.6 = 150.4 t

When steel is smelted from cast iron, a carbon removal process takes place. The iron mass remains constant.

Let’s denote the mass of carbon in steel as x. This x is 1.5% by weight of the steel. The mass of steel is m (Fe) + m (C in steel) = 150.4 + x. Let’s make the equation:

0.015 = x / (150.4 + x)

We solve the equation.

x = 2.29 t

m (steel) = 150.4 + 2.29 = 152.69 t

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