Question

У Миши было на 16 карандашей меньше, чем у Вики. Когда Миша отдал 2 карандаша Вике, у нее стало в 2 раза больше карандашей, чем у Миши. Сколько карандашей было у Миши сначала?​

Answer 1

Ответ: 22 какрандаша.

Пошаговое объяснение:

                 Миша               Вика

Было         х - 16                   х

Стало      х - 16 - 2             х + 2 и это в 2 раза больше, чем у Миши

Сотавим и решим уравнение:

2(х - 18) = х + 2,

2х - 36 = х + 2,

2х - х = 2 + 36,

х = 38.

Значит, у Вики было 38 карандашей, а у Миши 38 - 16 = 22 (кар.).

Answer 2

Problem Analysis

To solve this problem, we need to determine the initial number of pencils that Misha had. We are given the following information:

- Misha had 16 pencils fewer than Vika. - When Misha gave 2 pencils to Vika, Vika had twice as many pencils as Misha.

Let's assume that the initial number of pencils Misha had is represented by the variable `x`. We can use this information to set up the following equations:

1. Misha had 16 pencils fewer than Vika: `x = (Vika's pencils) - 16` 2. When Misha gave 2 pencils to Vika, Vika had twice as many pencils as Misha: `2 * (Misha's pencils - 2) = Vika's pencils + 2`

We can solve this system of equations to find the value of `x`, which represents the initial number of pencils Misha had.

Solution

Let's solve the system of equations step by step.

1. Misha had 16 pencils fewer than Vika: `x = (Vika's pencils) - 16`

2. When Misha gave 2 pencils to Vika, Vika had twice as many pencils as Misha: `2 * (Misha's pencils - 2) = Vika's pencils + 2`

Let's substitute the value of `(Vika's pencils)` from equation 1 into equation 2:

`2 * (Misha's pencils - 2) = (x + 16) + 2`

Simplifying the equation:

`2 * Misha's pencils - 4 = x + 18`

Rearranging the equation:

`2 * Misha's pencils = x + 22`

Now, let's substitute the value of `x` from equation 1 into the rearranged equation:

`2 * Misha's pencils = (Vika's pencils) - 16 + 22`

Simplifying the equation:

`2 * Misha's pencils = (Vika's pencils) + 6`

Since we know that `(Vika's pencils) = Misha's pencils + 16`, we can substitute this value into the equation:

`2 * Misha's pencils = Misha's pencils + 16 + 6`

Simplifying the equation:

`2 * Misha's pencils = Misha's pencils + 22`

Subtracting `Misha's pencils` from both sides of the equation:

`Misha's pencils = 22`

Therefore, Misha initially had 22 pencils.

Answer

Misha initially had 22 pencils.