A coaxial cable 10 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of cable.
x + (2/3)x = 10
(5/3)x = 10
x = 10 / (5/3)
x = 10 * (3/5)
x = 30/5 = 6
The longer piece is 6 feet long.
Shorter piece = (2/3) * 6
To solve this problem, we can set up an equation using the given information.
Let's assume the length of the shorter piece of cable is "x" feet.
Then, the length of the longer piece of cable will be "2x/3" feet.
According to the problem statement, the total length of the coaxial cable is 10 feet. Therefore, we can write the equation:
x + 2x/3 = 10
To solve this equation, we need to eliminate the fraction. We can do this by multiplying every term in the equation by 3:
3(x) + 3(2x/3) = 3(10)
3x + 2x = 30
5x = 30
Dividing both sides of the equation by 5 gives us:
x = 30/5
x = 6
Hence, the length of the shorter piece of cable is 6 feet.