Question

В новом учебнике по математике всего 91 задача. Юра начал их решать по утрам с 8 сентября. Начиная с 9 сентября он решает на одну задачу меньше, чем предыдущим утром, пока задачи не закончатся. Вечером 10 сентября Юра понял, что в учебнике осталось еще 46 нерешенных задач. Какого сентября он дорешает все задачи в учебнике? Скажите ответ срочно пожалуста

Answer 1

Ответ: за 3 дня

Пошаговое объяснение:

1) 91 - 46 = 45 (прочитал)

2) 45 - 22 = 23 (за 1 день)

3) 23 - 1 = 22 (за 2 день)

короче дальше сам

Answer 2

Problem Analysis

To solve this problem, we need to determine the date on which Yura finishes solving all the problems in the textbook. We know that Yura started solving the problems on September 8th and that each day he solves one less problem than the previous day until he finishes all the problems. We also know that on the evening of September 10th, Yura realized that there were still 46 unsolved problems in the textbook.

Solution

Let's break down the problem step by step:

1. Yura started solving the problems on September 8th. 2. On September 9th, he solved one less problem than the previous day. 3. On September 10th, he solved one less problem than the previous day. 4. On the evening of September 10th, Yura realized that there were still 46 unsolved problems in the textbook.

To find the date on which Yura finishes solving all the problems, we need to determine how many problems he solved on September 8th, September 9th, and September 10th.

Let's assume that Yura solved x problems on September 8th. Then, on September 9th, he solved x - 1 problems, and on September 10th, he solved x - 2 problems.

We know that on the evening of September 10th, Yura realized that there were still 46 unsolved problems in the textbook. This means that the total number of problems in the textbook is equal to the number of problems Yura solved plus the 46 unsolved problems.

Let's set up an equation to solve for x:

x + (x - 1) + (x - 2) + 46 = 91

Simplifying the equation:

3x + 43 = 91

3x = 48

x = 16

Therefore, Yura solved 16 problems on September 8th, 15 problems on September 9th, and 14 problems on September 10th.

To find the date on which Yura finishes solving all the problems, we need to count the number of days from September 10th until Yura finishes solving the remaining 14 problems.

Calculation

Since Yura solves one less problem each day, we can calculate the number of days it takes for him to solve the remaining 14 problems using the formula for the sum of an arithmetic series:

n = (2 * a + d * (n - 1)) / 2

Where: - n is the number of terms (days) - a is the first term (14 problems) - d is the common difference (-1 problem per day)

Plugging in the values:

14 = (2 * 14 + (-1) * (n - 1)) / 2

Simplifying the equation:

14 = 28 - n + 1

n = 15

Therefore, it will take Yura 15 more days to solve the remaining 14 problems.

Final Answer

To find the date on which Yura finishes solving all the problems, we need to add 15 days to September 10th.

Adding 15 days to September 10th, we get:

September 25th.

Therefore, Yura will finish solving all the problems in the textbook on September 25th.

I hope this helps! Let me know if you have any further questions.