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 [tex]x[/tex], so we must first find that. The equation for the length of rope is:
[tex]25 = 4x+3x+4[/tex]
The terms with [tex]x[/tex] can be combined:
[tex]25 = 7x+4[/tex]
Now, take 4 from both sides:
[tex]7x=21[/tex]
And divide by 7:
[tex]x=3[/tex]
Now we just use the value found for [tex]x[/tex] to find the lengths of the rope:
[tex]4x=4(3)=12\\3x=3(3)=9[/tex]
To check the answer, we can make sure the three lengths sum to 25 feet:
[tex]12+9+4=25[/tex]
Which it does. So the three lengths are 12 feet, 9 feet and 4 feet.
