Question

В коробке находятся белые, чёрные и красные кубики. Всего 50 штук. Белых в одиннадцать раз больше, чем чёрных. Красных меньше белых, но больше чёрных. Сколько красных кубиков находится в коробке?

Answer 1

Problem Analysis

We are given a box containing white, black, and red cubes. The total number of cubes is 50. The number of white cubes is eleven times the number of black cubes. The number of red cubes is less than the number of white cubes but greater than the number of black cubes. We need to determine the number of red cubes in the box.

Solution

Let's assume the number of black cubes in the box is x.

According to the given information, the number of white cubes is eleven times the number of black cubes, so the number of white cubes is 11x.

The number of red cubes is less than the number of white cubes but greater than the number of black cubes. Therefore, the number of red cubes is between x and 11x.

Since the total number of cubes is 50, we can write the equation:

x + 11x + (number of red cubes) = 50

Simplifying the equation, we get:

12x + (number of red cubes) = 50

Now, we need to solve this equation to find the value of x and the number of red cubes.

Solving the Equation

To solve the equation, we can use algebraic manipulation.

12x + (number of red cubes) = 50

Rearranging the equation, we get:

(number of red cubes) = 50 - 12x

Since the number of red cubes is between x and 11x, we can substitute the value of (number of red cubes) in terms of x:

x < (number of red cubes) < 11x

Substituting the value of (number of red cubes) from the equation, we get:

x < 50 - 12x < 11x

Simplifying the inequality, we get:

13x > 50 > x

Dividing the inequality by 13, we get:

x > 50/13 > x/13

Since x represents the number of black cubes, it must be a whole number. Therefore, we can conclude that x = 4.

Substituting the value of x in the equation, we get:

(number of red cubes) = 50 - 12(4) = 50 - 48 = 2

Therefore, there are 2 red cubes in the box.

Answer

There are 2 red cubes in the box.