Question

В новом учебнике по математике всего 91 задача. Юра начал их решать по утрам с 7 сентября. Начиная с 8 сентября он решает на одну задачу меньше, чем предыдущим утром, пока задачи не закончатся. Вечером 9 сентября Юра понял, что в учебнике осталось еще 46 нерешенных задач. Какого сентября он дорешает все задачи в учебнике?​

Answer 1

Відповідь:

13 сентября Юра дорешает все задачи в учебнике.

Покрокове пояснення:

7 сентября Юра решил Х задач, 8 сентября - ( Х - 1 ), 9 сентября - ( Х - 2 ).

За три дня Юра решил Х + ( Х - 1 ) + ( Х - 2 ) = 3Х - 3 = 91 - 46 = 45 задач.

Х = 16 задач - Юра решил 7 сентября, ( Х - 1 ) = 15 задач - Юра решил 8 сентября, ( Х - 2 ) = 14 задач - Юра решил 9 сентября.

10 сентября Юра решит 14 - 1 = 13 задач и останется решить 46 - 13 = 33 задачи.

11 сентября Юра решит 13 - 1 = 12 задач и останется решить 33 - 12 = 21 задачу.

12 сентября Юра решит 12 - 1 = 11 задач и останется решить 21 - 11 = 10 задач.

13 сентября Юра решит 11 - 1 = 10 задач и останется решить 10 - 11 = 0 задач - все задачи решены.

Answer 2

Ответ:

Пошаговое объяснение:

45

Потому что на день меньше если так то 44

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 7th and each day he solves one less problem than the previous day until he finishes all the problems. We are also given that on the evening of September 9th, 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 7th, Yura starts solving the problems. Let's assume he solves x problems on that day. 2. On September 8th, Yura solves one less problem than the previous day. So, he solves x - 1 problems on this day. 3. On September 9th, Yura solves one less problem than the previous day. So, he solves x - 2 problems on this day.

We are given that on the evening of September 9th, Yura realizes that there are still 46 unsolved problems in the textbook. This means that the sum of the problems solved on September 7th, 8th, and 9th is equal to the total number of problems in the textbook minus 46.

Mathematically, we can represent this as:

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

Simplifying the equation:

3x - 3 = 45

Adding 3 to both sides:

3x = 48

Dividing both sides by 3:

x = 16

Therefore, Yura solves 16 problems on September 7th.

To find the date on which Yura finishes solving all the problems, we need to determine how many days it takes for him to solve all the remaining problems after September 9th.

Since Yura solves one less problem each day, the number of problems he solves each day forms an arithmetic sequence. We can use the formula for the sum of an arithmetic sequence to find the total number of days it takes for Yura to solve all the remaining problems.

The formula for the sum of an arithmetic sequence is:

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

Where: - Sn is the sum of the first n terms - a is the first term - d is the common difference between terms - n is the number of terms

In this case, the first term (a) is x - 2, the common difference (d) is -1, and the sum (Sn) is 46.

Plugging in the values:

46 = (n/2)(2(x - 2) + (n-1)(-1))

Simplifying the equation:

46 = (n/2)(2x - 4 - n + 1)

46 = (n/2)(2x - n - 3)

Since we know that x = 16, we can substitute this value into the equation:

46 = (n/2)(2(16) - n - 3)

Simplifying further:

46 = (n/2)(32 - n - 3)

46 = (n/2)(29 - n)

To solve this equation, we can try different values for n until we find a solution that satisfies the equation. Let's start with n = 2:

46 = (2/2)(29 - 2)

46 = (1)(27)

This is not equal to 46, so n = 2 is not a solution. Let's try n = 3:

46 = (3/2)(29 - 3)

46 = (3/2)(26)

46 = (3/2)(13)

46 = 19.5

This is not equal to 46, so n = 3 is not a solution. Let's try n = 4:

46 = (4/2)(29 - 4)

46 = (4/2)(25)

46 = (4/2)(12.5)

46 = 25

This is not equal to 46, so n = 4 is not a solution. Let's try n = 5:

46 = (5/2)(29 - 5)

46 = (5/2)(24)

46 = (5/2)(12)

46 = 30

This is not equal to 46, so n = 5 is not a solution. Let's try n = 6:

46 = (6/2)(29 - 6)

46 = (6/2)(23)

46 = (6/2)(11.5)

46 = 34.5

This is not equal to 46, so n = 6 is not a solution. Let's try n = 7:

46 = (7/2)(29 - 7)

46 = (7/2)(22)

46 = (7/2)(11)

46 = 38.5

This is not equal to 46, so n = 7 is not a solution. Let's try n = 8:

46 = (8/2)(29 - 8)

46 = (8/2)(21)

46 = (8/2)(10.5)

46 = 42

This is not equal to 46, so n = 8 is not a solution. Let's try n = 9:

46 = (9/2)(29 - 9)

46 = (9/2)(20)

46 = (9/2)(10)

46 = 45

This is not equal to 46, so n = 9 is not a solution. Let's try n = 10:

46 = (10/2)(29 - 10)

46 = (10/2)(19)

46 = (10/2)(9.5)

46 = 47.5

This is not equal to 46, so n = 10 is not a solution. Let's try n = 11:

46 = (11/2)(29 - 11)

46 = (11/2)(18)

46 = (11/2)(9)

46 = 49.5

This is not equal to 46, so n = 11 is not a solution. Let's try n = 12:

46 = (12/2)(29 - 12)

46 = (12/2)(17)

46 = (12/2)(8.5)

46 = 51

This is not equal to 46, so n = 12 is not a solution. Let's try n = 13:

46 = (13/2)(29 - 13)

46 = (13/2)(16)

46 = (13/2)(8)

46 = 52

This is not equal to 46, so n = 13 is not a solution. Let's try n = 14:

46 = (14/2)(29 - 14)

46 = (14/2)(15)

46 = (14/2)(7.5)

46 = 53

This is not equal to 46, so n = 14 is not a solution. Let's try n = 15:

46 = (15/2)(29 - 15)

46 = (15/2)(14)

46 = (15/2)(7)

46 = 52.5

This is not equal to 46, so n = 15 is not a solution. Let's try n = 16:

46 = (16/2)(29 - 16)

46 = (16/2)(13)

46 = (16/2)(6.5)

46 = 52

This is not equal to 46, so n = 16 is not a solution. Let's try n = 17:

46 = (17/2)(29 - 17)

46 = (17/2)(12)

46 = (17/2)(6)

46 = 51

This is not equal to 46, so n = 17 is not a solution. Let's try n = 18:

46 = (18/2)(29 - 18)

46 = (18/2)(11)

46 = (18/2)(5.5)

46 = 49.5

This is not equal to 46, so n = 18 is not a solution. Let's try n = 19:

46 = (19/2)(29 - 19)

46 = (19/2)(10)

46 = (19/2)(5)

46 = 47.5

This is not equal to 46, so n = 19 is not a solution. Let's try n = 20:

46 = (20/2)(29 - 20)

46 = (20/2)(9)

46 = (20/2)(4.5)

46 = 45

This is equal to 46, so n = 20 is a solution.

Therefore, it takes Yura 20 days to solve all the remaining problems in the textbook after September