13.035. A shoe factory completed $20 \%$ of the monthly plan in the first week, produced $120 \%$ of the amount of products made in the first week in the second week, and produced $60 \%$ of the products made in the first two weeks combined in the third week. What is the monthly production plan for shoes, if it is known that to complete it, it is necessary to manufacture 1480 pairs of shoes in the last week of the month?
## Solution.

Let $x$ be the monthly production plan for shoes. In the first week, the factory produced $0,2 x$ pairs of shoes, in the second week - $1,2 \cdot 0,2 x$; in the third week - $0,6(0,2 x+1,2 \cdot 0,2 x)$ pairs. According to the condition,

$0,2 x+1,2 \cdot 0,2 x+0,6(0,2 x+1,2 \cdot 0,2 x)+1480=x$, from which $x=5000$ pairs.

Answer: 5000.