a 28 ft rope is cut into 2 pieces. one is 3 feet longer than the other. how long are the pieces?
x + (x+3) = 28
2 x + 3 = 28
2x = 25
x = 12.5
x+3 = 15.5
find the value of n for which 4(n-4)+13=7n+3?
Let's solve this step-by-step:
Step 1: Let's assume the length of one piece is x ft.
Step 2: According to the problem, the other piece is 3 ft longer than the first piece, so its length would be (x + 3) ft.
Step 3: The sum of the lengths of the two pieces should be equal to the total length of the rope, which is 28 ft.
So, we can write the equation: x + (x + 3) = 28.
Step 4: Simplifying the equation, we get 2x + 3 = 28.
Step 5: Subtracting 3 from both sides, the equation becomes 2x = 25.
Step 6: Dividing both sides by 2, we have x = 12.5.
Step 7: Therefore, one piece is 12.5 ft long, and the other piece is 3 ft longer, which is 15.5 ft long.
So, the two pieces are 12.5 ft and 15.5 ft long, respectively.
To find the lengths of the two pieces of rope, let's denote the length of one piece as x feet.
According to the given information, the other piece is 3 feet longer than this piece. So, the length of the other piece can be represented as (x + 3) feet.
Now, we need to consider the sum of the lengths of the two pieces, which should equal the total length of the rope, which is 28 feet.
Therefore, we can set up the equation:
x + (x + 3) = 28
Simplifying the equation:
2x + 3 = 28
2x = 28 - 3
2x = 25
x = 25 / 2
x = 12.5
So, one piece of rope has a length of 12.5 feet, and the other piece, which is 3 feet longer, has a length of (12.5 + 3) = 15.5 feet.