Kate cut a 100-foot rope into two pieces. One piece was 5 feet longer than 4 times the length of the other. Find the length of each piece.
first, represent the unknowns:
let x = length of the 1st piece
let 4x + 5 = length of the 2nd piece (as the second statement of the problem says)
then set-up equation:
x + (4x + 5) = 100 *total length of the two pieces must be 100 ft
solve:
5x + 5 = 100
5x = 95
x = 19 ft
4x + 5 = 81 ft
so there,, =)
3456
Would it be the same if u used 4 times x or it has to be 4x?
A 23 inch rope is cut into 4 pieces.the first piece is 3 inches longer than the other three pieces of rope .what is the length of the longest piece of rope
19ft, 81ft
Let's assume the length of one piece of rope is "x" feet. According to the problem, the other piece is 5 feet longer than 4 times the length of the first piece.
So, the length of the second piece of rope is (4x + 5) feet.
Since Kate has cut a 100-foot rope into two pieces, the total length of the two pieces should add up to 100 feet:
x + (4x + 5) = 100
Now, we can solve this equation to find the value of "x."
Combining like terms, we get:
5x + 5 = 100
Subtracting 5 from both sides, we have:
5x = 95
Dividing both sides by 5, we get:
x = 19
So, one piece of the rope is 19 feet long, and the other piece is:
4x + 5 = 4(19) + 5 = 76 + 5 = 81 feet
Therefore, the length of each piece is 19 feet and 81 feet, respectively.