Question

РЕШИТЕ, ПОЖАЛУЙСТА, ЗАДАЧУ: В коробке лежат желтые и синие конусы, а также синие цилиндры. Конусов в два раза больше, чем цилиндров. Синих фигур в 5 раз больше, чем желтых. Какую часть от всех фигур составляют синие конусы?

Answer 1

Половину
g-желтые конусы
с- синие цилиндры
х- синие конусы
х+g=2c - по условию
с+х=5g - по условию
5g-x=c
10g-2x=2c
x+g=2c
вычитаем одно из другого
9g-3x=0
3g=x - то есть синих конусов в 3 раза больше чем желтых
х+g=2c - подставляем сюда равенство 3g=x нами полученное
4g = 2c
2g=c - то есть синих цилиндров в 2 раза больше чем желтых конусов
в общем короче всего у нас фигур получается х+с+g = 6 g, из них синие конусы - это 3g , соответственно ровно половина

Answer 2

Problem Analysis

We are given a box containing yellow and blue cones, as well as blue cylinders. The number of cones is twice the number of cylinders, and the number of blue figures is five times the number of yellow figures. We need to determine the fraction of all figures that are blue cones.

Solution

Let's assume that there are x yellow cones in the box. Since the number of cones is twice the number of cylinders, there are 2x cones in total. Additionally, the number of blue figures is five times the number of yellow figures, so there are 5x blue figures in total.

To find the fraction of all figures that are blue cones, we need to determine the ratio of the number of blue cones to the total number of figures.

The total number of figures in the box is the sum of the number of yellow cones, blue cones, and blue cylinders. Since we know that there are x yellow cones, 2x blue cones, and some number of blue cylinders, we can express the total number of figures as:

Total number of figures = x (yellow cones) + 2x (blue cones) + y (blue cylinders)

We don't know the exact number of blue cylinders, but we can express it in terms of x using the given information. Since the number of cones is twice the number of cylinders, we can write:

2x = y

Substituting this value back into the equation for the total number of figures, we get:

Total number of figures = x (yellow cones) + 2x (blue cones) + 2x (blue cylinders)

Simplifying the equation, we have:

Total number of figures = 5x

Therefore, the fraction of all figures that are blue cones is:

Fraction of blue cones = (2x) / (5x) = 2/5

So, 2/5 of all the figures in the box are blue cones.

Answer

The fraction of all figures that are blue cones is 2/5.