Question

Общая масса трёх деталей составляет 250 кг. Масса первой и второй деталей на 10 кг меньше массы третьей, а второй и третьей - на 110 кг больше массы первой. Найдите массу каждой детали.

Answer 1

1-хкг
2-укг
3-zкг
{x+y+z=250  (1)
{x+y-z=-10  (2)
{y+z-x=110  (3)
(1)+(2) 2x+2y=240⇒x+y=120
(2)+(3)  2y=100⇒y=50кг
x+50=120
x=120-50
x=70кг
120+z=250
z=250-120
z=130кг

Answer 2

Problem Analysis

We are given three parts with their respective masses. The total mass of the three parts is 250 kg. The mass of the first and second parts is 10 kg less than the mass of the third part, and the mass of the second and third parts is 110 kg more than the mass of the first part. We need to find the mass of each part.

Solution

Let's assume the mass of the first part is x kg. According to the given information, the mass of the second part is x + 110 kg, and the mass of the third part is x + 120 kg.

The total mass of the three parts is 250 kg, so we can write the equation:

x + (x + 110) + (x + 120) = 250

Simplifying the equation:

3x + 230 = 250

Subtracting 230 from both sides:

3x = 20

Dividing both sides by 3:

x = 20/3

Therefore,