Question

Петя, Вася и Харитон ели яблоки. Петя и Вася съели вместе в два раза больше чем Харитон, а Харитон и Петя вместе съели в 6 раз больше чем Вася. сколько яблок съел каждый из мальчиков, если всего они съели 105 яблок?

Answer 1

Ответ 32 и 96...................

Answer 2

Problem Analysis

We are given that Petya, Vasya, and Khariton ate apples. Petya and Vasya together ate twice as many apples as Khariton, and Khariton and Petya together ate six times as many apples as Vasya. We need to determine how many apples each of the boys ate if they ate a total of 105 apples.

Solution

Let's assume that Khariton ate x apples.

According to the given information: - Petya and Vasya together ate twice as many apples as Khariton, so they ate 2x apples. - Khariton and Petya together ate six times as many apples as Vasya, so they ate 6y apples, where y is the number of apples Vasya ate.

We also know that the total number of apples eaten is 105. Therefore, we can write the equation:

x + 2x + 6y = 105

Simplifying the equation, we get:

3x + 6y = 105

To solve this equation, we need another equation. Let's use the fact that Petya and Vasya together ate twice as many apples as Khariton:

2x = 2 * x

Simplifying, we get:

2x = 2x

This equation doesn't provide any additional information, so we can ignore it.

Now, let's solve the equation 3x + 6y = 105 for x and y.

Solution Steps

1. Solve the equation 3x + 6y = 105 for x in terms of y. 2. Substitute the value of x in terms of y into the equation x + 2x + 6y = 105. 3. Solve the resulting equation for y. 4. Substitute the value of y into the equation x + 2x + 6y = 105 to find x. 5. Calculate the number of apples each boy ate.

Detailed Solution

Step 1: Solve the equation 3x + 6y = 105 for x in terms of y.

To solve for x, we can rearrange the equation as follows:

3x = 105 - 6y

Dividing both sides by 3, we get:

x = (105 - 6y) / 3

Step 2: Substitute the value of x in terms of y into the equation x + 2x + 6y = 105.

Substituting the value of x, we get:

(105 - 6y) / 3 + 2 * (105 - 6y) / 3 + 6y = 105

Simplifying the equation, we get:

(105 - 6y + 2 * (105 - 6y) + 18y) / 3 = 105

Step 3: Solve the resulting equation for y.

Expanding the equation, we get:

(105 - 6y + 210 - 12y + 18y) / 3 = 105

Combining like terms, we get:

(315 - y) / 3 = 105

Multiplying both sides by 3, we get:

315 - y = 315

Subtracting 315 from both sides, we get:

-y = 0

Multiplying both sides by -1, we get:

y = 0

Step 4: Substitute the value of y into the equation x + 2x + 6y = 105 to find x.

Substituting y = 0, we get:

x + 2x + 6 * 0 = 105

Simplifying the equation, we get:

3x = 105

Dividing both sides by 3, we get:

x = 35

Step 5: Calculate the number of apples each boy ate.

We have found that Khariton ate x = 35 apples, Vasya ate y = 0 apples, and Petya ate 2x = 2 * 35 = 70 apples.

Therefore, the number of apples each boy ate is: - Khariton: 35 apples - Vasya: 0 apples - Petya: 70 apples

Answer

Based on the given information, Khariton ate 35 apples, Vasya ate 0 apples, and Petya ate 70 apples.