B4. After a forest fire, campers were reforesting the area and planted 960 trees. They planted 5 times as many pines as firs and 6 times as many spruces as firs. How many trees of each species did they plant? What percentage of the planted trees are firs?

## Solutions and Scoring

## A contestant who arrives at the solution by any correct method (even if the scoring guide does not provide for it) receives all possible points.

For a correct method, any procedure that

- sensibly takes into account the wording of the problem,
- leads to the solution of the problem,
- is mathematically correct and complete.

A contestant who has only partially solved the problem, from otherwise correct steps in solving but does not show the path to the final solution of the problem, cannot receive more than half of the possible points.

## PART I

The correct answers are recorded in the table. A correct answer by the contestant is scored with 2 points, an incorrect answer with -1 point, and a blank field in the table with 0 points.

| Task | $\mathrm{A} 1$ | $\mathrm{~A} 2$ | $\mathrm{~A} 3$ | $\mathrm{~A} 4$ | $\mathrm{~A} 5$ | $\mathrm{~A} 6$ | $\mathrm{~A} 7$ | $\mathrm{~A} 8$ | $\mathrm{~A} 9$ | $\mathrm{~A} 10$ |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| Answer | $\mathrm{D}$ | $\mathrm{C}$ | $\mathrm{C}$ | $\mathrm{A}$ | $\mathrm{E}$ | $\mathrm{C}$ | $\mathrm{D}$ | $\mathrm{E}$ | $\mathrm{E}$ | $\mathrm{C}$ |
B4. Let the number of spruces be denoted by $x$. Then the number of pines is $5 x$, and the number of firs is $6 x$. We write the equation $960=x+5 x+6 x$, whose solution is $x=80$. This means that the campers planted 80 spruces, 400 pines, and 480 firs. The planted spruces represent $\frac{80}{960}=\frac{1}{12}$ of all the trees, which is $\frac{100}{12}=\frac{25}{3} \%$ or $8, \overline{3} \%$ of all the trees.

## Scoring: Total: 5 points

![](https://cdn.mathpix.com/cropped/2024_06_07_41ad29ae87bc570f2592g-7.jpg?height=60&width=1642&top_left_y=547&top_left_x=273)
Answer in terms of: They planted:

![](https://cdn.mathpix.com/cropped/2024_06_07_41ad29ae87bc570f2592g-7.jpg?height=49&width=1628&top_left_y=655&top_left_x=277)

![](https://cdn.mathpix.com/cropped/2024_06_07_41ad29ae87bc570f2592g-7.jpg?height=52&width=1639&top_left_y=705&top_left_x=274)

![](https://cdn.mathpix.com/cropped/2024_06_07_41ad29ae87bc570f2592g-7.jpg?height=51&width=1639&top_left_y=754&top_left_x=277)

Answer, e.g.: They planted $8, \overline{3} \%$ (or $\frac{25}{3} \%$) of spruces......................................... 1 p Note: If the result is not accurately written, 0 p.