Question

85 баллов Бабушка весь год вязала варежки. В январе бабушка связала 8 варежек, а в каждый из остальных месяцев она вязала на одинаковое число варежек больше, чем в предыдущем. Сколько варежек связала бабушка в мае, если всего с января по декабрь включительно она связала 294варежки?(с решением)

Answer 1

Ответ: 20 шт

Объяснение:

Смотри вложение

Answer 2

Problem Analysis

We are given that a grandmother knitted mittens throughout the year. In January, she knitted 8 mittens, and in each subsequent month, she knitted a number of mittens that was greater than the previous month. We need to determine how many mittens she knitted in May, given that she knitted a total of 294 mittens from January to December (inclusive).

Solution

To solve this problem, we can use a simple arithmetic progression. Let's denote the number of mittens knitted in January as 'a', and the common difference between the number of mittens knitted in consecutive months as 'd'. We can set up the following equation:

a + (a + d) + (a + 2d) + ... + (a + 10d) = 294

The left side of the equation represents the sum of an arithmetic progression with 11 terms (January to December inclusive). We can simplify this equation to:

11a + 55d = 294

Now, we need to find the values of 'a' and 'd' that satisfy this equation. We can use the given information that the number of mittens knitted in each subsequent month is one more than the previous month. This means that the common difference 'd' is equal to 1.

Substituting 'd' into the equation, we get:

11a + 55 = 294

Simplifying further:

11a = 294 - 55 11a = 239

Dividing both sides by 11, we find:

a = 239 / 11 a ≈ 21.73

Since the number of mittens must be a whole number, we can round 'a' to the nearest whole number. Therefore, 'a' is approximately 22.

Now that we know the value of 'a', we can find the number of mittens knitted in May. Since May is the fifth month, we can use the formula for the nth term of an arithmetic progression:

aₙ = a + (n - 1)d

Substituting the values, we get:

a₅ = 22 + (5 - 1) * 1 a₅ = 22 + 4 a₅ = 26

Therefore, the grandmother knitted 26 mittens in May.

Answer

The grandmother knitted 26 mittens in May.

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