B4. In every cubic meter of water flowing into Cold Cave, there are $75 \mathrm{~g}$ of arsenic dissolved.

A How many grams of arsenic are in $350 \ell$ of water flowing into Cold Cave? Write the result to two decimal places.

B In a reservoir filled with water from Cold Cave, there are $35 \mathrm{~g}$ of dissolved arsenic. What is the volume of the reservoir? Write the result to the nearest liter.

C Cold Cave is adorned by a massive, 1000-kilogram stalactite, entirely composed of arsenic. At least how many cubic meters of water have flowed into Cold Cave for this much arsenic to have precipitated out of the water?

## 10th Mathematics Knowledge Competition for Vocational School Students

Regional Competition, March 31, 2010

## Solutions to Problems and Scoring

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

A correct method is considered any procedure that

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

$V$ in the table are the correct answers to the multiple-choice questions. Each correct answer is scored with 2 points, an incorrect answer with $-0.5$ points, and if the question is not answered, 0 points.

| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| C | B | C | C | B | E | E | A | B | D |
B4. For calculations, we use a reasoning approach. In 350 liters of water, there is $\frac{350 \ell \cdot 75 \mathrm{~g}}{1000 \ell}=26.25 \mathrm{~g}$ of arsenic. Arsenic with a mass of $35 \mathrm{~g}$ is in $\frac{35 \mathrm{~g} \cdot 1000 \ell}{75 \mathrm{~g}}=466.67 \ell \approx 467 \ell$ of water. For 1000 kilograms of arsenic to precipitate, at least $\frac{1000000 \mathrm{~g} \cdot 1000 \ell}{75 \mathrm{~g}}=13333333.33 \ell \approx 13333 \mathrm{~m}^{3}$ of water has flowed in.

A Calculated mass of arsenic: $26.25 \mathrm{~g}$. ........................................................ 1 point

B Calculated volume of water containing $35 \mathrm{~g}$ of arsenic: $467 \ell$. ...................... 2 points Note: An incorrect or improperly rounded answer gives the contestant only 1 point.

C Calculated volume of water from which $1000 \mathrm{~kg}$ of arsenic has precipitated: $13333 \mathrm{~m}^{3} \ldots 1$ point Written answer, e.g.: At least $13333 \mathrm{~m}^{3}$ of water has flowed in. ................................ 1 point