## Task 2 - V10922

According to our seven-year plan, the industrial production of the German Democratic Republic will increase significantly. The total industrial production will grow by 88% from 1958 to 1965. The production of means of production (i.e., raw materials, machinery, equipment for industry, agriculture, and transportation, etc.) will increase by 95%, while the production of consumer goods (i.e., goods intended for the needs of the population) will increase by 77%.

What percentage of the total industrial production did the production of means of production account for in 1958? What percentage will it account for in 1965?
Sure, here is the translated text:

---

|  | 1958 | 1965 |
| :--- | :--- | :--- |
| Total Industrial Production | 100 | 188 |
| Production of Means of Production | $x$ | $\frac{195}{100} x$ |
| Production of Consumer Goods | $y$ | $\frac{177}{100} y$ |

Total Industrial Production = Production of Means of Production + Production of Consumer Goods

$$
100=x+y \quad(1) \quad 100 \cdot 108=195 \cdot x+177 \cdot y
$$

From (I) + (II) it follows: $195 x+177(100-x)=18800$, i.e., $x=61.1$.

In 1958, the share of the production of means of production was approximately $61.1\%$ of the total production. From the table, it follows:

Let $p$ be the required percentage for the production of means of production in 1965, then it must hold:

$$
188: 100=\frac{195}{100} \cdot 61.1: p \Rightarrow p=63.4
$$

In 1965, the share of the production of means of production is 63.4% of the total industrial production.