Let's denote the length of red wire as x meters and the length of yellow wire as y meters.
Given that a person requires 5 meters of yellow wire for every 8 meters of red wire, we can write the equation:
y = (5/8) * x
We are also given that the cost of red wire is 7 per meter and of yellow wire is 6 per meter. The total cost of the electrical wire is 8686.
The cost of red wire is 7x and the cost of yellow wire is 6y. The total cost equation is:
7x + 6y = 8686
Now, we can substitute y = (5/8) * x into the total cost equation and solve for x:
7x + 6 * (5/8) * x = 8686
7x + (30/8) * x = 8686
(56/8) * x + (30/8) * x = 8686
(86/8) * x = 8686
10.75 * x = 8686
x = 8686 / 10.75
x ≈ 807.7209
Now that we have the value of x, we can find y using y = (5/8) * x:
y = (5/8) * 807.7209
y ≈ 504.8256
Therefore, the length of the red wire is approximately 807.72 meters, and the length of the yellow wire is approximately 504.83 meters.