Question

Бабушки собрали 2 мешка яблок. В первом лежит половина того, что во втором мешке и еще 5 яблок. А во втором мешке столько яблок, сколько в первом и еще 10. Сколько яблок в двух мешках?

Answer 1

Ответ:

50 яблок

Пошаговое объяснение:

х - яблок в 1-м мешке

у - яблок во 2-м мешке

х = 0,5у + 5

у = х + 10

Подставим 2-е выражение в 1-е

х = 0,5(х + 10) + 5

х = 0,5х + 5 + 5

0,5х = 10

х = 20

у = 20 + 10 = 30

В двухмешках х + у = 20 + 30 = 50 (яблок)

Answer 2

Problem Analysis

We are given that two grandmothers collected 2 bags of apples. In the first bag, there are half as many apples as in the second bag, plus an additional 5 apples. In the second bag, there are as many apples as in the first bag, plus an additional 10 apples. We need to determine the total number of apples in both bags.

Solution

Let's assume the number of apples in the second bag is x. According to the problem, the number of apples in the first bag is half of x, plus 5. Therefore, the number of apples in the first bag can be expressed as (x/2) + 5.

Similarly, the number of apples in the second bag is x, plus 10.

To find the total number of apples in both bags, we need to add the number of apples in the first bag to the number of apples in the second bag.

Let's calculate the total number of apples:

Total number of apples = (x/2) + 5 + x + 10

Simplifying the equation:

Total number of apples = (x/2) + x + 15

To solve for x, we can multiply the equation by 2 to eliminate the fraction:

2 * Total number of apples = x + 2x + 30

Simplifying further:

2 * Total number of apples = 3x + 30

Now, we can solve for x:

3x = 2 * Total number of apples - 30

x = (2 * Total number of apples - 30) / 3

Let's substitute the value of x back into the equation for the total number of apples to find the final answer.

Calculation

Let's calculate the total number of apples using the given information.

The total number of apples in both bags is equal to (x/2) + 5 + x + 10.

Substituting the value of x:

Total number of apples = ((2 * Total number of apples - 30) / 3) / 2 + 5 + (2 * Total number of apples - 30) / 3 + 10

Simplifying the equation:

Total number of apples = (2 * Total number of apples - 30) / 6 + 5 + (2 * Total number of apples - 30) / 3 + 10

Combining like terms:

Total number of apples = (2 * Total number of apples - 30 + 10 + 30) / 6 + 5

Simplifying further:

Total number of apples = (2 * Total number of apples + 10) / 6 + 5

Multiplying both sides of the equation by 6 to eliminate the fraction:

6 * Total number of apples = 2 * Total number of apples + 10 + 30

Simplifying:

6 * Total number of apples = 2 * Total number of apples + 40

Subtracting 2 * Total number of apples from both sides of the equation:

4 * Total number of apples = 40

Dividing both sides of the equation by 4:

Total number of apples = 40 / 4

Total number of apples = 10

Therefore, there are 10 apples in the two bags combined.

Answer

There are 10 apples in the two bags combined.