1. A batch of shoes, purchased for 180 thousand rubles, was sold in the first week at a price higher than the purchase price by $25 \%$, then the markup was reduced to $16 \%$ of the purchase price; and the entire batch of shoes was sold for $20 \%$ more than it was purchased for. For what amount was the shoes sold in the first week?
# Solution:

$x$ thousand rubles - the purchase cost of shoes sold in the first week, $y$ - the remainder.

$$
\left\{\begin{array} { c } 
{ x + y = 180 } \\
{ 25 x + 16 y = 20 ( x + y ) ; }
\end{array} \left\{\begin{array} { c } 
{ 5 x = 4 y , } \\
{ x + 5 / 4 x = 180 ; }
\end{array} \left\{\begin{array}{l}
x=80 \\
y=100
\end{array}\right.\right.\right.
$$

Revenue from sales in the first week is $80 \cdot 1.25=100$ thousand rubles.

Answer: 100 thousand rubles