Question

Проволоку разрезали на 6 частей.Перва часть меньше четвёртой на 1,2м и больше пятой на 3,8м. Вторая часть больше шестой на 2,7м и меньше пятой на 4,3м и равна третьей части. Найдите длину проволоки, если длина четвёртойчасти равна18,3м.

Answer 1

длина 4 части = 18,3

18,3-1,2=17,1 (м) - длина 1 части

17,1-3,8=13,3 (м) - длина 5 части

13,3-4,3=9 (м) - длина 2 части

9-2,7=6,3 (м) - длина 6 части

3 часть  = 2 части = 9 (м) 

18,3+17,1+13,3+9+6,3+9=73 (м) - длина проволоки

 

Answer 2

Problem Analysis

We are given that a wire has been cut into 6 parts. The first part is 1.2m shorter than the fourth part and 3.8m longer than the fifth part. The second part is 2.7m longer than the sixth part and 4.3m shorter than the fifth part. Additionally, the second part is equal in length to the third part. We need to find the length of the wire if the fourth part is 18.3m long.

Solution

Let's assign variables to the lengths of the wire parts: - Let x be the length of the first part. - Let y be the length of the second part. - Let z be the length of the third part. - Let w be the length of the fourth part. - Let v be the length of the fifth part. - Let u be the length of the sixth part.

Based on the given information, we can write the following equations:

1. The first part is 1.2m shorter than the fourth part: x = w - 1.2. 2. The first part is 3.8m longer than the fifth part: x = v + 3.8. 3. The second part is 2.7m longer than the sixth part: y = u + 2.7. 4. The second part is 4.3m shorter than the fifth part: y = v - 4.3. 5. The second part is equal in length to the third part: y = z. 6. The fourth part is 18.3m long: w = 18.3.

We can solve this system of equations to find the values of x, y, z, v, and u, and then calculate the length of the wire by summing all the parts.

Solution Steps

1. Substitute equation 6 into equation 1 to eliminate w: x = 18.3 - 1.2. 2. Substitute equation 6 into equation 2 to eliminate w: x = v + 3.8. 3. Substitute equation 6 into equation 4 to eliminate w: y = v - 4.3. 4. Substitute equation 6 into equation 5 to eliminate w: y = z. 5. Substitute equation 6 into equation 3 to eliminate w: y = u + 2.7. 6. Substitute equation 4 into equation 5 to eliminate v: y = y - 4.3. 7. Substitute equation 5 into equation 3 to eliminate y: z = y. 8. Substitute equation 3 into equation 2 to eliminate z: y = z + 3.8. 9. Substitute equation 3 into equation 1 to eliminate z: x = z + 3.8. 10. Substitute equation 3 into equation 6 to eliminate z: u = 18.3 - 1.2. 11. Substitute equation 3 into equation 4 to eliminate z: y = y - 4.3. 12. Substitute equation 3 into equation 5 to eliminate z: y = y.

Now we have a system of equations with only one variable, y. We can solve for y and then substitute the values back into the other equations to find the lengths of the other parts.

Solution Steps Continued

13. Substitute equation 7 into equation 11 to eliminate y: 0 = -4.3. 14. Since equation 13 is always true, the system of equations is dependent and has infinitely many solutions. This means that the lengths of the wire parts cannot be determined uniquely.

Therefore, we cannot find the length of the wire based on the given information.

Please let me know if I can help you with anything else.