5. In two orchards, they harvested a total of 315 tons of fruit in the first year. The following year, the total yield increased by $40 \%$. In the first orchard, the yield increased by $25 \%$, and in the second orchard, it increased by $50 \%$. How many tons of fruit were harvested in each orchard in the first year?

## You have 120 minutes to solve the problems.

Solve the problems independently on the provided paper, with each problem on a separate page. Do not sign the sheets, write only your code. Write your answers with a pen, clearly and neatly. Draw graphs with a pencil. If you solve a problem in multiple ways, clearly indicate which solution the evaluator should grade. If you make a mistake, cross out the incorrect part.

Each problem's solution will be graded from 0 to 6 points.

The National Competition Committee wishes you great success.

## Problems for 2nd Year

![](https://cdn.mathpix.com/cropped/2024_06_07_6d1b766ff5bddd57ba61g-03.jpg?height=177&width=417&top_left_y=360&top_left_x=1482)
5. We write the expression $315+40\%$ of 315 and calculate that it is 441. Considering the yield in the 1st garden $x+\frac{25}{100} x=x+\frac{x}{4}=\frac{5 x}{4}$, and the yield in the second garden $(315-x)+\frac{50}{100}(315-x)=$ $472.5-1.5 x$. We add the yield from both gardens $\frac{5 x}{4}+472.5-1.5 x=441$. Solving the equation, we get the solution $x=126$. In the first garden, 126 tons of fruit grew, and in the second, 189 tons.

Calculation of $315+40\%$ of $315=441$ 1 point

Calculation for the 1st garden $x+\frac{25}{100} x=x+\frac{x}{4}=\frac{5 x}{4}$ 1 point

Calculation for the 2nd garden $(315-x)+\frac{50}{100}(315-x)=472.5-1.5 x \ldots$ 1 point

Writing the equation $\frac{5 x}{4}+472.5-1.5 x=441 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$

![](https://cdn.mathpix.com/cropped/2024_06_07_6d1b766ff5bddd57ba61g-08.jpg?height=48&width=1636&top_left_y=273&top_left_x=207)

![](https://cdn.mathpix.com/cropped/2024_06_07_6d1b766ff5bddd57ba61g-08.jpg?height=60&width=1642&top_left_y=318&top_left_x=204)

## Second Year