## 69. Math Puzzle $2 / 71$

In a Siemens-Martin furnace, 20 t of steel with a $0.5 \%$ carbon content is melted together with 5 t of gray cast iron with a $5 \%$ carbon content.

What percent of carbon does the mixture contain?
The carbon content of the mixture is $x \%$, i.e., $25 \mathrm{t}$ of the mixture contains $\frac{25 x}{100} \mathrm{t}$ of carbon. 20 $\mathrm{t}$ of steel contain $\frac{20 \cdot 0.05}{100} \mathrm{t}$ and the $5 \mathrm{t}$ of gray cast iron contain $\frac{5 \cdot 0.5}{100}$ carbon. The sum of the carbon amounts of the parts must equal the total amount of carbon.

$$
\frac{20 \cdot 0.05}{100}+\frac{5 \cdot 0.5}{100}=\frac{25 \cdot x}{100} \rightarrow x=1.4
$$

The mixture thus contains $1.4 \%$ carbon.