## Task 3 - 070613

In a storage, a total of $2170 \mathrm{~kg}$ of grain was stored. There were exactly 11 sacks of wheat at $80 \mathrm{~kg}$ each, 6 sacks of barley, and 12 sacks of corn. Each sack of barley contained $5 \mathrm{~kg}$ more than each sack of corn. How many kilograms of corn were stored in the storage?
The mass of the wheat is $11 \cdot 80 \mathrm{~kg}=880 \mathrm{~kg}$, so the combined mass of barley ($g$ per sack) and corn ($m$ per sack) is $1290 \mathrm{~kg}$. Since $g=m+5$, the equation for both (in kilograms) is:

$$
6 g+12 m=1290 \quad ; \quad 6 \cdot(m+5)+12 m=1290=18 m+30
$$

From this, the mass of corn per sack is $m=70 \mathrm{~kg}$, and thus the mass of barley per sack is $g=75 \mathrm{~kg}$. Since there are 12 sacks of corn, their total mass is $12 \cdot 70 \mathrm{~kg}=840 \mathrm{~kg}$.