Question

A rope 25 feet long is cut into 3 pieces. The first piece is 4x feet long, the second piece is 3x feet long and the third is is 4 feet long. Find the length of each price of rope

Answer 1

Answer:

The first piece is 12 feet long, the second is 9 feet long, and the third is 4 feet long.

Step-by-step explanation:

The original rope is 25 feet in length. Two pieces are dependant on the value of $x$, so we must first find that. The equation for the length of rope is:

$25 = 4x+3x+4$

The terms with $x$ can be combined:

$25 = 7x+4$

Now, take 4 from both sides:

$7x=21$

And divide by 7:

$x=3$

Now we just use the value found for $x$ to find the lengths of the rope:

$4x=4(3)=12\\3x=3(3)=9$

To check the answer, we can make sure the three lengths sum to 25 feet:

$12+9+4=25$

Which it does. So the three lengths are 12 feet, 9 feet and 4 feet.