B4. The diagram shows the amounts of pocket money that students receive from their parents in one month.

A. How many students receive at least 31 EUR in pocket money?

B. What percentage of students receive less than 21 EUR in monthly pocket money?

C. Calculate the average value of pocket money in whole euros for the students shown in the diagram.

![](https://cdn.mathpix.com/cropped/2024_06_07_3ad088fae533eb6a81abg-4.jpg?height=766&width=597&top_left_y=1259&top_left_x=1312)

Monthly pocket money in EUR

## 12th Mathematics Competition for Vocational School Students

Regional Competition, March 28, 2012

## Solutions to Problems and Scoring

A contestant who arrives at the solution by any correct method (even if not specified in the scoring) will receive 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.

In section A, a correct answer will be scored with two points, while an incorrect answer will result in a deduction of half a point. To avoid any potential negative final score, each contestant is given an initial 5 points.

The table below lists the correct answers to the multiple-choice questions.

| A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| A | B | D | B | D | C | D | B | E | C |
B4. From the diagram, we read the claims: 20 students receive at least 31 EUR pocket money and 13 students receive less than 21 EUR pocket money (which is approximately $28.9 \%$).

The average pocket money is $\frac{4 \cdot 5.5 + 9 \cdot 15.5 + 12 \cdot 25.5 + 11 \cdot 35.5 + 9 \cdot 45.5}{45} \approx 28$ EUR.
A. 20 students receive at least 31 EUR pocket money. ....................................................... 1 p
B. $28.9 \%$ of students receive less than 21 EUR pocket money. ........................................... 2 p

C. The average pocket money is 28 EUR. .............................................................. 2 p