Question

В коробке лежат 105 кубиков трех цветов. Желтых на 3 больше, чем зеленых. Количество зеленых относится к количеству синих как 5:7. Сколько кубиков каждого цвета в коробке?

Answer 1

Неправильно в книжке 4 варинта ответа а) 4 и2 б) 2 и 4 в) 21 и 7 г) 7 и 21

Answer 2

Problem Analysis

We are given a box containing 105 cubes of three different colors: yellow, green, and blue. The number of yellow cubes is 3 more than the number of green cubes. The ratio of green cubes to blue cubes is 5:7. We need to determine the number of cubes of each color in the box.

Solution

Let's denote the number of yellow cubes as Y, the number of green cubes as G, and the number of blue cubes as B.

From the given information, we can form the following equations:

1. Y + G + B = 105 (since the total number of cubes is 105) 2. Y = G + 3 (since the number of yellow cubes is 3 more than the number of green cubes) 3. G/B = 5/7 (since the ratio of green cubes to blue cubes is 5:7)

To solve these equations, we can use substitution or elimination method. Let's use the substitution method.

From equation 3, we can rewrite it as G = (5/7)B.

Substituting this value of G in equation 2, we get Y = (5/7)B + 3.

Now, substituting the values of Y and G in equation 1, we get:

(5/7)B + 3 + (5/7)B + B = 105

Simplifying the equation:

(10/7)B + 3 + B = 105

(17/7)B = 102

Multiplying both sides by 7/17:

B = (7/17) * 102

B ≈ 42

Now, substituting the value of B in equation 2, we get:

G = (5/7) * 42

G ≈ 30

Finally, substituting the values of G and B in equation 1, we get:

Y + 30 + 42 = 105

Y ≈ 33

Therefore, there are approximately 33 yellow cubes, 30 green cubes, and 42 blue cubes in the box.

Answer: There are approximately 33 yellow cubes, 30 green cubes, and 42 blue cubes in the box.