Question

3. В первом ящике 8 кг винограда, что в 1 1/7 раза больше, чем во втором, и в 1 1/8 раза меньше, чем в третьем. Сколько килограммов винограда в трех ящиках?

Answer 1

1) 8 : 1 1/7 = 7кг - во 2 ящике
2) 8 * 1 1/8 = 9 кг - в 3-м ящике
3) 8 + 7+ 9 =24 кг - в 3-х ящиках

Answer 2

Problem Analysis

We are given information about three boxes of grapes. The weight of grapes in the first box is 8 kg, which is 1 1/7 times more than the weight in the second box. The weight in the first box is also 1 1/8 times less than the weight in the third box. We need to find the total weight of grapes in the three boxes.

Solution

Let's assume the weight of grapes in the second box is x kg.

According to the given information: - The weight of grapes in the first box is 1 1/7 times more than the weight in the second box. This can be expressed as: 8 = x + (1 1/7)x. - The weight of grapes in the first box is 1 1/8 times less than the weight in the third box. This can be expressed as: 8 = (1 1/8)(x + (1 1/7)x).

To solve these equations, we can simplify the fractions and solve for x.

Calculation

Let's calculate the value of x using the given equations:

Equation 1: 8 = x + (1 1/7)x - Convert 1 1/7 to an improper fraction: 1 1/7 = 8/7 - Simplify the equation: 8 = (8/7)x + (8/7)x - Combine like terms: 8 = (16/7)x - Multiply both sides by 7/16 to isolate x: x = (8 * 7) / 16 = 3.5 kg

Equation 2: 8 = (1 1/8)(x + (1 1/7)x) - Convert 1 1/8 to an improper fraction: 1 1/8 = 9/8 - Simplify the equation: 8 = (9/8)(x + (8/7)x) - Combine like terms: 8 = (9/8)(15/7)x - Multiply both sides by 8/9 to isolate x: x = (8 * 15) / (9 * 7) = 1.90476 kg (rounded to 5 decimal places)

Now that we have the value of x, we can calculate the weight of grapes in the third box: Weight in the third box = x + (1 1/7)x = 3.5 + (1 1/7)(3.5) = 3.5 + (8/7)(3.5) = 3.5 + 4 = 7.5 kg

Answer

The weight of grapes in the three boxes is as follows: - First box: 8 kg - Second box: 3.5 kg - Third box: 7.5 kg

Therefore, the total weight of grapes in the three boxes is 8 + 3.5 + 7.5 = 19 kg.