## Task 4 - 160624

A feed mixture for breeding boars consists of oat groats, wheat bran, barley groats, minerals, and water, and is composed as follows: half of the mixture is oat groats, $\frac{1}{10}$ of the mixture is wheat bran, $\frac{1}{4}$ of the mixture is barley groats, $\frac{1}{100}$ of the mixture is minerals, and the rest is water.

Calculate (in $\mathrm{kg}$) the amount of water contained in $35 \mathrm{~kg}$ of this feed mixture!
According to the task, $35 \, \text{kg}$ of the mixture mentioned in the task contains exactly $17.5 \, \text{kg}$ of oat bran because $\frac{1}{2} \cdot 35 = 17.5$,

exactly $3.5 \, \text{kg}$ of wheat bran because $\frac{1}{10} \cdot 35 = 3.5$,

exactly $8.75 \, \text{kg}$ of barley bran because $\frac{1}{4} \cdot 35 = 8.75$,

and exactly $0.35 \, \text{kg}$ of minerals because $\frac{1}{100} \cdot 35 = 0.35$.

This totals $17.5 + 3.5 + 8.75 + 0.35 = 30.1 \, \text{kg}$. Since $35 - 30.1 = 4.9$, exactly $4.9 \, \text{kg}$ of water remain as the water content of this feed mixture.

Solutions of the II. Round 1976 taken from [5]

### 3.18 XVII. Olympiad 1977

### 3.18.1 I. Round 1977, Class 6