13.159. Three departments of the institute have submitted applications for the purchase of additional equipment for laboratories. The cost of the equipment in the application of the first department is $45\%$ of the application of the second department, and the cost of the equipment in the application of the second department is $80\%$ of the application of the third department. The cost of the equipment in the application of the third department exceeds the application of the first by 640 thousand rubles. What is the total cost of the equipment in the applications of all three departments?
## Solution.

Let $x, y, z$ thousand rubles be the cost of equipment in the applications of the first,

second, and third departments, respectively. According to the conditions $\left\{\begin{array}{l}x=0.45 y, \\ y=0.8 z, \\ z=x+640,\end{array}\right.$ from

which $x=360$ thousand rubles, $y=800$ thousand rubles, $z=1000$ thousand rubles. The total cost of the equipment in the applications of all three departments is $360+800+$ $+1000=2160$ (thousand rubles)

Answer: 2 million 160 thousand rubles.