Question

Кольцо состоит из золота и серебра. 0.25 части массы кольца составляет серебро. Найдите массу кольца,если известно,что серебра на 4 грамма меньше золота. Задача по математике 5 класс.

Answer 1

Х  -  масса кольца
0,25х  -  серебро

1) х - 0,25х = 0,75х - составляет золото
2) 0,75х - 0,25х = 4
    0,5х = 4
    х = 4 : 0,5
    х = 8 г - масса кольца.

Если через Х не проходили, то другое решение :

1) 1 - 0,25 = 0,75 - масса золота
2) 0,75 - 0,25 = 0,5 - разница между серебром и золотом (= 4г)
3) 4 : 0,5 = 8 г - масса кольца.

Answer 2

Problem Analysis

To solve this problem, we need to find the mass of the ring given that it is made of gold and silver, and 0.25 parts of the ring's mass is silver. We also know that the silver is 4 grams less than the gold.

Solution

Let's assume the mass of the gold in the ring is x grams. Since the silver is 4 grams less than the gold, the mass of the silver would be x - 4 grams.

According to the problem statement, 0.25 parts of the ring's mass is silver. This means that the mass of the silver is 0.25 times the total mass of the ring. Therefore, we can write the equation:

x - 4 = 0.25(x + (x - 4))

Now, let's solve this equation to find the mass of the gold and silver in the ring.

Solving the Equation

Expanding the equation, we get:

x - 4 = 0.25(2x - 4)

Simplifying further:

x - 4 = 0.5x - 1

Bringing like terms to one side:

x - 0.5x = -1 + 4

Simplifying:

0.5x = 3

Dividing both sides by 0.5:

x = 6

So, the mass of the gold in the ring is 6 grams.

Now, let's find the mass of the silver:

x - 4 = 6 - 4 = 2

Therefore, the mass of the silver in the ring is 2 grams.

Finding the Total Mass of the Ring

To find the total mass of the ring, we need to add the mass of the gold and the mass of the silver:

Total mass = Mass of gold + Mass of silver = 6 + 2 = 8 grams

Therefore, the mass of the ring is 8 grams.

Answer

The mass of the ring is 8 grams.

Note: The sources provided did not contain specific information related to this problem. The solution was derived using mathematical calculations.