B3. The diagram shows the distribution of bronze, silver, and gold medals at a competition.

(a) What is the value of $x$? (see image)

(b) Write the ratio of gold, silver, and bronze medals in the smallest possible natural numbers.

![](https://cdn.mathpix.com/cropped/2024_06_07_b93fa657b92bc897cb7bg-05.jpg?height=417&width=423&top_left_y=126&top_left_x=1496)

(c) At the competition, 84 medals were awarded. How many bronze, how many silver, and how many gold medals were awarded?

(d) How many grams does a bronze medal weigh if it has the shape of a cylinder with a diameter of $7 \mathrm{~cm}$ and a height of 3 $\mathrm{mm}$? The density of bronze is $8700 \frac{\mathrm{kg}}{\mathrm{m}^{3}}$.

## 21st Mathematics Knowledge Competition for Vocational School Students National Competition, May 15, 2021

## Problems for 3rd Year

Time for solving: 90 minutes. In section A, we will award two points for a correct answer, while we will deduct half a point for an incorrect answer. Enter the answers for section A in the left table. In section B, we will award up to seven points for a correct answer.
![](https://cdn.mathpix.com/cropped/2024_06_07_b93fa657b92bc897cb7bg-06.jpg?height=162&width=1198&top_left_y=590&top_left_x=444)
B3. The value of $x$ is calculated considering the equation $(5 x)^{\circ}+(4 x)^{\circ}+90^{\circ}=360^{\circ}$. The solution to the equation is $x=30^{\circ}$.

The ratio of gold, silver, and bronze medals is Z:S:B $=5: 3: 4$.

Considering the ratio of gold, silver, and bronze medals and the number of medals awarded, we write the equation $5 t+3 t+4 t=84$. Using the solution to the equation $t=7$, we calculate the number of gold medals: $5 \cdot 7=35$, silver medals: $3 \cdot 7=21$, and bronze medals: $4 \cdot 7=28$.

The volume of a bronze medal is $V=\pi \cdot 3.5^{2} \cdot 0.3=11.55 \mathrm{~cm}^{3}=1.155 \cdot 10^{-5} \mathrm{~m}^{3}$. The mass of the medal is $m=1.155 \cdot 10^{-5} \cdot 8700=0.1004 \mathrm{~kg}=100.4 \mathrm{~g}$.

(a) Calculation of the value $x=30^{\circ}$. ..........................................................................................

(b) Writing the ratio of gold, silver, and bronze medals: $\mathrm{Z}: \mathrm{S}: \mathrm{B}=5: 3: 4 . \ldots . .2 \mathrm{t}$

(c) Calculation of the number of awarded gold (35), silver (21), and bronze (28) medals. ............ 2 t

(d) Calculation of the mass of a bronze medal to the nearest gram: 100 g. ................................ 2 t

## 21st Mathematics Knowledge Competition for Vocational School Students  National Competition, May 15, 2021

## Solutions to Problems for 3rd Year

| A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| C | B | B | A | D | B | B | C |