Question

Решите пожалуйста задачу с подробным объяснением . ( дам 15 баллов ) Одну третью часть фишек , то есть 12 , Ермек дал Алине , а одну треть оставшихся фишек и ещё 1 фишку дал Артёму . После этого у Ермека осталось 15 фишек . Всего у Ермека было фишек ? ( мы с одноклассницой спорим у всех разные ответы , помогите пожалуйста)

Answer 1

1/3 * 12 = 36 фишек - было всего

отдал Алине 12, осталось 36 - 12 = 24
1/3 остатка = 1/3 * 24 = 8
8 + 1 = 9 фишек - отдал Артему
36 - 12 - 9 = 15 фишек - осталось

Всего у Ермека было 36 фишек.
Этот ответ можно дать сразу после предложения "Одну третью часть фишек , то есть 12", остальное - либо для запутывания, либо для проверки.

Answer 2

Problem Analysis

We are given that Ermek gave 12 chips to Alina and then gave one-third of the remaining chips plus one chip to Artem. After this, Ermek had 15 chips left. We need to determine the total number of chips Ermek had initially.

Solution

Let's assume that the initial number of chips Ermek had is represented by the variable `x`.

According to the problem, Ermek gave 12 chips to Alina. So, the number of chips remaining with Ermek after giving chips to Alina is `x - 12`.

Next, Ermek gave one-third of the remaining chips plus one chip to Artem. This can be represented as `(1/3)*(x - 12) + 1`.

Finally, we are given that Ermek had 15 chips left. So, we can set up the equation:

`(1/3)*(x - 12) + 1 = 15`

To solve this equation, we can follow these steps:

1. Distribute the `(1/3)` term: `(1/3)*x - 4 + 1 = 15` 2. Simplify: `(1/3)*x - 3 = 15` 3. Add 3 to both sides: `(1/3)*x = 18` 4. Multiply both sides by 3 to eliminate the fraction: `x = 54`

Therefore, the total number of chips Ermek initially had is 54.

Answer

Ermek initially had 54 chips.

Verification

Let's verify our answer using the given information.

According to the problem, Ermek gave 12 chips to Alina, which leaves him with 54 - 12 = 42 chips.

Next, Ermek gave one-third of the remaining chips plus one chip to Artem. One-third of 42 is 14, and adding one chip gives a total of 15 chips given to Artem.

After giving chips to Artem, Ermek had 42 - 15 = 27 chips left.

Therefore, our answer is consistent with the given information, and Ermek initially had 54 chips.