1. The businessman bought pullovers and paid 960 thousand for them. In the store, he sold them for 12 thousand each. The profit he made from selling all the pullovers was equal to the amount he paid for 60 pullovers. How many pullovers did he buy? Write down the answer.
1. Denote that the business management has purchased $x$ pullovers at a purchase price of $c$. Then it holds that $x \cdot c=960000$ and $x \cdot 12000=960000+60 c$. From the second equation, we express $c=200 x-16000$ and substitute it into the first, which we rearrange into the quadratic equation $200 x^{2}-16000 x-960000=0$, simplify to $x^{2}-80 x-4800=0$ and factorize $(x-120)(x+40)=0$. The only meaningful solution to the equation is $x=120$. The business management has purchased 120 pullovers.

Choice of unknowns: $x$ - number of pullovers, $c$ - purchase price, $d$ - profit from selling one pullover.

![](https://cdn.mathpix.com/cropped/2024_06_07_06886e410b39c0216094g-10.jpg?height=57&width=1636&top_left_y=2313&top_left_x=210)

Correct solving of the system of equations ......................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_06886e410b39c0216094g-10.jpg?height=51&width=1642&top_left_y=2419&top_left_x=207)

Answer: The business management has purchased 120 pullovers............................................................