Question

N9 3 В новом учебнике по математике всего 91 задача. Юра начал их решать по утрам с6 сентября. Начиная с 7 сентября он решает на одну задачу меньше, чем предыдущим утром, пока задачи не закончатся. Вечером 8 сентября Юра понял, что в учебнике осталось еще 46 нерешенных задач. Какого сентября он дорешает все задачи в учебнике? Помогите

Answer 1

Ответ:

24 октября

Пошаговое объяснение:

Answer 2

Ответ:

11 сентября

Пошаговое объяснение:

16,15,14,13,12,11,10

Answer 3

Problem Analysis

To solve this problem, we need to determine the date on which Yura finishes solving all the problems in the textbook. We are given that Yura starts solving the problems on September 6th and each morning he solves one less problem than the previous morning until he finishes all the problems. We are also given that on the evening of September 8th, Yura realizes that there are still 46 unsolved problems in the textbook.

Solution

Let's break down the problem step by step:

1. On September 6th, Yura starts solving the problems. We know that there are a total of 91 problems in the textbook.

2. Starting from September 7th, Yura solves one less problem each morning than the previous morning until he finishes all the problems.

3. On the evening of September 8th, Yura realizes that there are 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 Yura solves each morning and how many days it takes for him to finish all the problems.

Let's calculate the number of problems Yura solves each morning:

- On September 6th, Yura solves x problems. - On September 7th, Yura solves x - 1 problems. - On September 8th, Yura solves x - 2 problems.

We know that on the evening of September 8th, Yura realizes that there are still 46 unsolved problems in the textbook. This means that the sum of the problems Yura solved from September 6th to September 8th is equal to 91 - 46 = 45.

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

x + (x - 1) + (x - 2) = 45

Simplifying the equation:

3x - 3 = 45

3x = 48

x = 16

Therefore, Yura solves 16 problems on September 6th, 15 problems on September 7th, and 14 problems on September 8th.

Now, let's calculate the number of days it takes for Yura to finish all the problems:

To find the total number of problems Yura solves, we can use the formula for the sum of an arithmetic series:

S = (n/2)(a + l)

where S is the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, the first term is 16, the last term is 1, and the sum is 91.

91 = (n/2)(16 + 1)

91 = (n/2)(17)

91 = 8.5n

n = 10.7

Since the number of days cannot be a fraction, we round up to the nearest whole number. Therefore, it takes Yura 11 days to finish all the problems.

To determine the date on which Yura finishes all the problems, we add 11 days to September 8th:

September 8th + 11 days = September 19th.

Therefore, Yura finishes all the problems in the textbook on September 19th.

Answer

Yura finishes solving all the problems in the textbook on September 19th.