Question

Настя планувала Розв‘язати 60 задач за 6 днів але розв‘язувала щодня на 2 задачі більше, ніж планувала. За скільки днів Настя розв‘язала всі задачі? А) 5 днів Б) 4 дні В) 3 дні Г) 8 днів

Answer 1

Ответ: А) 5 днів

Пошаговое объяснение:

60 : 6 = 10 задач планувала розв‘язувати за один день

10 + 2= 12 задач розв‘язувала щодня

60 : 12 = 5 днів за стільки  Настя розв‘язала всі задачі

Answer 2

Ответ:

Пошаговое объяснение:

60÷6= 10 задач щодня планувала

10+2=12задач решала

60÷12=5 дн

Answer 3

To solve this problem, we can set up an equation based on the given information. Let's denote the number of days it took Nastya to solve all the problems as "x".

According to the problem, Nastya solved 2 more problems each day than she planned. So, on the first day, she solved 2 more problems than planned, on the second day, she solved 4 more problems than planned, and so on.

We can set up the equation as follows:

2 + 4 + 6 + ... + 2x = 60

To simplify the equation, we can factor out 2:

2(1 + 2 + 3 + ... + x) = 60

Now, we need to find the value of x that satisfies this equation. We can use the formula for the sum of an arithmetic series to simplify further:

2 * (x * (x + 1)) / 2 = 60

Simplifying the equation, we have:

x * (x + 1) = 60 / 2

x * (x + 1) = 30

Expanding the equation, we have:

x^2 + x = 30

Rearranging the equation, we have:

x^2 + x - 30 = 0

Now, we can solve this quadratic equation to find the value of x. Factoring the equation, we have:

(x + 6)(x - 5) = 0

So, x can be either -6 or 5. Since the number of days cannot be negative, we can conclude that Nastya solved all the problems in 5 days.

Therefore, the correct answer is A) 5 days.