Question

Виталику нужно решить 95 задач, а Мише 60. Виталик ежедневно решает 7 задач, а Миша 6.Через сколько дней у Виталика останется вдвое больше не решенных задач, чем у Миши, если они начали решать в один и тот же день?

Answer 1

Х - количество дней
За это время Виталик решит 7х задач,
 а Миша 6х задачВиталику
останется решить 95-7х задач,
а Мише 60-6х задач
95-7х = 2(60-6х)
95-7х=120-12х
12х-7х=120-95
5х=25х=5 (дней)
Ответ: 5 дней

Answer 2

Problem Analysis

To solve this problem, we need to determine the number of days it will take for Vitalik to have twice as many unsolved problems as Misha, given that they both start solving problems on the same day.

We are given the following information: - Vitalik needs to solve 95 problems. - Misha needs to solve 60 problems. - Vitalik solves 7 problems per day. - Misha solves 6 problems per day.

Let's break down the problem and find a solution.

Solution

To find the number of days it will take for Vitalik to have twice as many unsolved problems as Misha, we can set up the following equation:

Vitalik's unsolved problems - Misha's unsolved problems = 2 * Misha's unsolved problems

Let's denote the number of days it will take as x.

Vitalik's unsolved problems after x days: 95 - 7x Misha's unsolved problems after x days: 60 - 6x

Setting up the equation:

95 - 7x - (60 - 6x) = 2(60 - 6x)

Simplifying the equation:

95 - 7x - 60 + 6x = 120 - 12x

Combining like terms:

35 - x = 120 - 12x

Bringing x terms to one side:

11x - x = 120 - 35

Simplifying:

10x = 85

Dividing both sides by 10:

x = 8.5

Since we cannot have half a day, we round up to the nearest whole number. Therefore, it will take approximately 9 days for Vitalik to have twice as many unsolved problems as Misha.

Answer

It will take approximately 9 days for Vitalik to have twice as many unsolved problems as Misha if they start solving problems on the same day.