Question

Масса болта с гайкой равна 49 г,а масса четырёх болтов на 70 г больше масс пяти гаек.Чему равна масса одного болта и масса одной гайки? (Решить задачу системой уравнений )

Answer 1

X - маса болта
y - маса гайки

x+y=49
4x-5y=70

Решив систему имеем
35 г - маса болта
14 г - маса гайки

Answer 2

Problem Analysis

We are given that the combined mass of a bolt and a nut is 49 g. The combined mass of four bolts is 70 g more than the combined mass of five nuts. We need to find the mass of one bolt and the mass of one nut. We can solve this problem using a system of equations.

Solution

Let's assume the mass of one bolt is x g and the mass of one nut is y g.

From the given information, we can set up the following equations:

Equation 1: x + y = 49 (The combined mass of a bolt and a nut is 49 g)

Equation 2: 4x - 5y = 70 (The combined mass of four bolts is 70 g more than the combined mass of five nuts)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From Equation 1, we can express y in terms of x:

y = 49 - x

Substituting this value of y into Equation 2:

4x - 5(49 - x) = 70

Simplifying the equation:

4x - 245 + 5x = 70

9x - 245 = 70

9x = 315

x = 35

Now, substituting the value of x back into Equation 1 to find y:

35 + y = 49

y = 14

Therefore, the mass of one bolt is 35 g and the mass of one nut is 14 g.

Answer

The mass of one bolt is 35 g and the mass of one nut is 14 g.