Question

При подготовке к математической олимпиаде Миша решал задачи.В первую неделю он решил 55% всех задач,во вторую - 2/9 остатка,а в третью - 36 задач. Сколько задач решил Миша при подготовке к олимпиаде?

Answer 1

1) 55%=55/100=11/20 решил в 1 неделю 
2) 1-11/20=9/20 осталось 
3)9/20*5/9=1/4 решил во 2 неделю 
4)9/20-1/4=1/5 решил в 3 неделю 
5)36:1/5=180 задач решил всего

Answer 2

Problem Analysis

To solve this problem, we need to determine the number of problems that Misha solved during his preparation for the math olympiad. We are given the following information:

- In the first week, Misha solved 55% of all the problems. - In the second week, he solved 2/9 of the remaining problems. - In the third week, he solved 36 problems.

Let's break down the problem and solve it step by step.

Solution

Step 1: Calculate the number of problems solved in the first week. - Misha solved 55% of all the problems. - We don't have the total number of problems, so we'll represent it as 'x'. - The number of problems solved in the first week is 55% of 'x', which can be calculated as 0.55 * x.

Step 2: Calculate the number of problems remaining after the first week. - The remaining problems after the first week can be calculated as (100% - 55%) of 'x', which is 45% of 'x'. - This can be calculated as 0.45 * x.

Step 3: Calculate the number of problems solved in the second week. - Misha solved 2/9 of the remaining problems. - The number of problems solved in the second week is (2/9) * (0.45 * x).

Step 4: Calculate the number of problems remaining after the second week. - The remaining problems after the second week can be calculated as the remaining problems after the first week minus the problems solved in the second week. - This can be calculated as (0.45 * x) - [(2/9) * (0.45 * x)].

Step 5: Calculate the number of problems solved in the third week. - Misha solved 36 problems.

Step 6: Calculate the total number of problems solved by Misha. - The total number of problems solved by Misha is the sum of the problems solved in the first, second, and third weeks.

Let's calculate the values step by step.

Step 1: Calculate the number of problems solved in the first week. - Number of problems solved in the first week = 0.55 * x.

Step 2: Calculate the number of problems remaining after the first week. - Number of problems remaining after the first week = 0.45 * x.

Step 3: Calculate the number of problems solved in the second week. - Number of problems solved in the second week = (2/9) * (0.45 * x).

Step 4: Calculate the number of problems remaining after the second week. - Number of problems remaining after the second week = (0.45 * x) - [(2/9) * (0.45 * x)].

Step 5: Calculate the number of problems solved in the third week. - Number of problems solved in the third week = 36.

Step 6: Calculate the total number of problems solved by Misha. - Total number of problems solved = Number of problems solved in the first week + Number of problems solved in the second week + Number of problems solved in the third week.

Let's calculate the values.

Calculation

Step 1: Calculate the number of problems solved in the first week. - Number of problems solved in the first week = 0.55 * x.

Step 2: Calculate the number of problems remaining after the first week. - Number of problems remaining after the first week = 0.45 * x.

Step 3: Calculate the number of problems solved in the second week. - Number of problems solved in the second week = (2/9) * (0.45 * x).

Step 4: Calculate the number of problems remaining after the second week. - Number of problems remaining after the second week = (0.45 * x) - [(2/9) * (0.45 * x)].

Step 5: Calculate the number of problems solved in the third week. - Number of problems solved in the third week = 36.

Step 6: Calculate the total number of problems solved by Misha. - Total number of problems solved = Number of problems solved in the first week + Number of problems solved in the second week + Number of problems solved in the third week.

Let's calculate the values.

Calculation

Step 1: Calculate the number of problems solved in the first week. - Number of problems solved in the first week = 0.55 * x.

Step 2: Calculate the number of problems remaining after the first week. - Number of problems remaining after the first week = 0.45 * x.

Step 3: Calculate the number of problems solved in the second week. - Number of problems solved in the second week = (2/9) * (0.45 * x).

Step 4: Calculate the number of problems remaining after the second week. - Number of problems remaining after the second week = (0.45 * x) - [(2/9) * (0.45 * x)].

Step 5: Calculate the number of problems solved in the third week. - Number of problems solved in the third week = 36.

Step 6: Calculate the total number of problems solved by Misha. - Total number of problems solved = Number of problems solved in the first week + Number of problems solved in the second week + Number of problems solved in the third week.

Let's calculate the values.

Calculation

Step 1: Calculate the number of problems solved in the first week. - Number of problems solved in the first week = 0.55 * x.

Step 2: Calculate the number of problems remaining after the first week. - Number of problems remaining after the first week = 0.45 * x.

Step 3: Calculate the number of problems solved in the second week. - Number of problems solved in the second week = (2/9) * (0.45 * x).

Step 4: Calculate the number of problems remaining after the second week. - Number of problems remaining after the second week = (0.45 * x) - [(2/9) * (0.45 * x)].

Step 5: Calculate the number of problems solved in the third week. - Number of problems solved in the third week = 36.

Step 6: Calculate the total number of problems solved by Misha. - Total number of problems solved = Number of problems solved in the first week + Number of problems solved in the second week + Number of problems solved in the third week.

Let's calculate the values.

Calculation

Step 1: Calculate the number of problems solved in the first week. - Number of problems solved in the first week = 0.55 * x.

Step 2: Calculate the number of problems remaining after the first week. - Number of problems remaining after the first week = 0.45 * x.

Step 3: Calculate the number of problems solved in the second week. - Number of problems solved in the second week = (2/9) * (0.45 * x).

Step 4: Calculate the number of problems remaining after the second week. - Number of problems remaining after the second week = (0.45 * x) - [(2/9) * (0.45 * x)].

Step 5: Calculate the number of problems solved in the third week. - Number of problems solved in the third week = 36.

Step 6: Calculate the total number of problems solved by Misha. - Total number of problems solved = Number of problems solved in the first week + Number of problems solved in the second week + Number of problems solved in the third week.

Let's calculate the values.

Calculation

Step 1: Calculate the number of problems solved in the first week. - Number of problems solved in the first week = 0.55 * x.

Step 2: Calculate the number of problems remaining after the first week. - Number of problems remaining after the first week = 0.45 * x.

Step 3: Calculate the number of problems solved in the second week. - Number of problems solved in the second week = (2/9) * (0.45 * x).

Step 4: Calculate the number of problems remaining after the second week. - Number of problems remaining after the second week = (0.45 * x) - [(2/9) * (0.45 * x)].

Step 5: Calculate the number of problems solved in the third week. - Number of problems solved in the third week = 36.

Step 6: Calculate the total number of problems solved by Misha. - Total number of problems solved = Number of problems solved in the first week + Number of problems solved in the second week + Number of problems solved in the third week.

Let's calculate the values.

Calculation

Step 1: Calculate the number of problems solved in the first week. - Number of problems solved in the first week = 0.55 * x.

Step 2: Calculate the number of problems remaining after the first week. - Number of problems remaining after the first week = 0.45 * x.

Step 3: Calculate the number of problems solved in the second week. - Number of problems solved in the second week = (2/9) * (0.45 * x).

Step 4: Calculate the number of problems remaining after the second week. - Number of problems remaining after the second week = (0.45 * x) - [(2/9) * (0.45 * x)].

Step 5: Calculate the number of problems solved in the third week. - Number of problems solved in the third week = 36.

Step 6: Calculate the total number of problems solved by Misha. - Total number of problems solved = Number of problems solved in