Question

В школьном туре математической олимпиады 1 и 2 места заняли 9 человек, что составило 30 процентов числа всех участников. 3 место заняли 33 1/3% остальных участников. Школьники не занявшие призовых мест получили похвальные грамоты.Сколько человек получило похвальные грамоты?

Answer 1

Всего учеников: 9 :30*100=30
3-е место: (30-9) :3 = 7
Грамотами: 30-9-7=14

Answer 2

Problem Analysis

We are given that in a school math competition, the first and second places were taken by 9 participants, which is 30% of all participants. The third place was taken by 33 1/3% of the remaining participants. We need to determine the number of participants who received certificates of commendation.

Solution

Let's assume the total number of participants in the competition is x.

From the given information, we know that 30% of all participants (x) took the first and second places, which is equal to 9 participants. This can be represented as an equation:

0.3x = 9 Solving this equation, we find that x = 30.

Now, we need to find the number of participants who took the third place. We are given that the third place was taken by 33 1/3% of the remaining participants. The remaining participants are the total participants (x) minus the participants who took the first and second places (9 participants). This can be represented as an equation:

0.333(x - 9) = 3 Solving this equation, we find that x = 18.

Therefore, the total number of participants in the competition is 18.

To find the number of participants who received certificates of commendation, we subtract the participants who took the first, second, and third places from the total number of participants:

Number of participants who received certificates of commendation = x - 9 - 3 = 18 - 9 - 3 = 6

Therefore, 6 participants received certificates of commendation.

Answer

The number of participants who received certificates of commendation is 6.