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

Accepted Solution

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.