5. If a pack of chewing gum were to increase in price by as many percent as its current price, we would have to pay 429 tolars for four packs. How much do these four packs cost us now? Write down your answer.[^0]

## You have $120 \mathrm{~min}$ for solving.

THE NATIONAL COMPETITION COMMITTEE WISHES YOU GREAT SUCCESS.

6th national mathematics knowledge competition for students of secondary technical and vocational schools Kranj, April 22, 2006

## PROBLEMS FOR 4th GRADE
5. Let the current price be x. We set up the equation $4 \cdot\left(x+x \cdot \frac{x}{100}\right)=429$. Simplifying the equation, we get $x^{2}+100 x-10725=0$. The solutions to the equation are $x=65$ and $x=-165$. We consider the positive solution. Four packages cost $4 \cdot 65=260$ tolars.

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-12.jpg?height=66&width=1642&top_left_y=732&top_left_x=207)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-12.jpg?height=52&width=1636&top_left_y=788&top_left_x=210)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-12.jpg?height=45&width=1636&top_left_y=840&top_left_x=210)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-12.jpg?height=49&width=1637&top_left_y=888&top_left_x=208)

Answer . .............................................................................................................

## Fourth Year