Question

Шесть гномов добыли 4320 алмазов. Первый, второй и третий добыли одинаковое количество алмазов. Четвертый в 2 раза больше чем каждый из них. Пятый в 3 раза больше. Шестой в 4 раза больше. Сколько алмазов добыл каждый из них?

Answer 1

Ответ:

Пошаговое объяснение:

1 = 2 = 3 = х алмазов

4 = 2х

5 = 3х

6 = 4х

х + х + х + 2х + 3х + 4х = 4320

12х = 4320

х = 4320 : 12

х = 360

1 = 2 = 3 (х) = 360 алмазов каждый

4 (2х) = 2 * 360 = 720 алмазов

5 (3х) = 3 * 360 = 1080 алмазов

6 (4х) = 4 * 360 = 1440 алмазов

360 + 360 + 360 + 720 + 1080 + 1440 = 4320

Answer 2

Calculation of the Number of Diamonds Each Dwarf Mined

To determine the number of diamonds each dwarf mined, let's analyze the information given in the question:

- The total number of diamonds mined by the six dwarfs is 4320. - The first, second, and third dwarfs mined the same amount of diamonds. - The fourth dwarf mined twice as many diamonds as each of the first three dwarfs. - The fifth dwarf mined three times as many diamonds as each of the first three dwarfs. - The sixth dwarf mined four times as many diamonds as each of the first three dwarfs.

Let's assign variables to represent the number of diamonds mined by each dwarf:

- Let's call the number of diamonds mined by the first, second, and third dwarfs "x." - The fourth dwarf mined twice as many diamonds as each of the first three dwarfs, so the number of diamonds mined by the fourth dwarf is "2x." - The fifth dwarf mined three times as many diamonds as each of the first three dwarfs, so the number of diamonds mined by the fifth dwarf is "3x." - The sixth dwarf mined four times as many diamonds as each of the first three dwarfs, so the number of diamonds mined by the sixth dwarf is "4x."

Now, we can set up an equation to solve for "x" and find the number of diamonds mined by each dwarf:

x + x + x + 2x + 3x + 4x = 4320

Simplifying the equation:

11x = 4320

Dividing both sides of the equation by 11:

x = 4320 / 11

Evaluating the division:

x ≈ 392.73

Since we are dealing with whole numbers, we can round the value of "x" to the nearest whole number:

x ≈ 393

Therefore, each of the first, second, and third dwarfs mined approximately 393 diamonds.

To find the number of diamonds mined by the fourth, fifth, and sixth dwarfs, we can substitute the value of "x" into the equations we established earlier:

- The fourth dwarf mined 2x = 2 * 393 = 786 diamonds. - The fifth dwarf mined 3x = 3 * 393 = 1179 diamonds. - The sixth dwarf mined 4x = 4 * 393 = 1572 diamonds.

Summary:

Based on the given information, the number of diamonds mined by each dwarf is approximately as follows: - First, second, and third dwarfs: 393 diamonds each. - Fourth dwarf: 786 diamonds. - Fifth dwarf: 1179 diamonds. - Sixth dwarf: 1572 diamonds.

Please note that the values provided are approximate due to rounding.