Question

Буратино получил от Мальвины задание вычислить 240 выражений за 10 дней,ежедневно поровну.Однако в день он вычисляется на 2 выражения меньше.Сколько всего выражений вычислил Буратино за 10 дней? (Реши двумя способами)

Answer 1

240:10=24 если бы он решал по плану мальвины 

24-2=22 сколько он решал на самом деле                                              22*10=220 столько он решил за  10 дней

Answer 2

Task Description

Буратино получил от Мальвины задание вычислить 240 выражений за 10 дней, ежедневно поровну. Однако в день он вычисляется на 2 выражения меньше. Сколько всего выражений вычислил Буратино за 10 дней? (Реши двумя способами)

Solution 1: Arithmetic Progression

To find the total number of expressions Buratino calculated in 10 days, we can use the concept of an arithmetic progression.

In this case, the first term (a) is the number of expressions calculated on the first day, the common difference (d) is the difference in the number of expressions calculated each day, and the number of terms (n) is the number of days.

Let's calculate the number of expressions calculated on the first day: - The total number of expressions is 240. - The number of days is 10. - The number of expressions calculated each day is equal, except for the last day when it is 2 less.

To find the number of expressions calculated on the first day, we can use the formula: a = (2 * total number of expressions - (n - 1) * d) / (2 * n) Substituting the given values: a = (2 * 240 - (10 - 1) * 2) / (2 * 10)

Now, let's calculate the number of expressions calculated on the first day using the formula: a = (480 - 18) / 20 = 462 / 20 = 23.1

Since we cannot have a fraction of an expression, we need to round down to the nearest whole number. Therefore, Buratino calculated 23 expressions on the first day.

Now, let's calculate the number of expressions calculated on the last day: - The number of expressions calculated each day is 2 less than the previous days. - The number of expressions calculated on the first day is 23.

To find the number of expressions calculated on the last day, we can use the formula: last day expressions = first day expressions - (n - 1) * d Substituting the given values: last day expressions = 23 - (10 - 1) * 2 = 23 - 18 = 5

Now, let's calculate the total number of expressions calculated in 10 days using the formula for the sum of an arithmetic progression: sum = (n / 2) * (first term + last term) Substituting the given values: sum = (10 / 2) * (23 + 5) = 5 * 28 = 140

Therefore, Buratino calculated a total of 140 expressions in 10 days.

Solution 2: Sum of an Arithmetic Series

Another way to solve this problem is by using the formula for the sum of an arithmetic series.

The formula for the sum of an arithmetic series is: sum = (n / 2) * (first term + last term) In this case, the first term (a) is the number of expressions calculated on the first day, the last term (l) is the number of expressions calculated on the last day, and the number of terms (n) is the number of days.

Let's calculate the number of expressions calculated on the first day: - The total number of expressions is 240. - The number of days is 10. - The number of expressions calculated each day is equal, except for the last day when it is 2 less.

To find the number of expressions calculated on the first day, we can use the formula: a = (2 * total number of expressions - (n - 1) * d) / (2 * n) Substituting the given values: a = (2 * 240 - (10 - 1) * 2) / (2 * 10)

Now, let's calculate the number of expressions calculated on the first day using the formula: a = (480 - 18) / 20 = 462 / 20 = 23.1

Since we cannot have a fraction of an expression, we need to round down to the nearest whole number. Therefore, Buratino calculated 23 expressions on the first day.

Now, let's calculate the number of expressions calculated on the last day: - The number of expressions calculated each day is 2 less than the previous days. - The number of expressions calculated on the first day is 23.

To find the number of expressions calculated on the last day, we can use the formula: last day expressions = first day expressions - (n - 1) * d Substituting the given values: last day expressions = 23 - (10 - 1) * 2 = 23 - 18 = 5

Now, let's calculate the total number of expressions calculated in 10 days using the formula for the sum of an arithmetic series: sum = (n / 2) * (first term + last term) Substituting the given values: sum = (10 / 2) * (23 + 5) = 5 * 28 = 140

Therefore, Buratino calculated a total of 140 expressions in 10 days.

In conclusion, Buratino calculated a total of 140 expressions in 10 days, both by using the concept of an arithmetic progression and the formula for the sum of an arithmetic series.