A 10 meter rope is cut into two pieces so that one piece is equal to 5 meters longer than 4 times the shorter piece find the lengths to both sides

shorter piece = X.

Longer piece = 4x + 5.

x + (4x+5) = 10.
X =
4x+ 5 =

To find the lengths of both sides, let's assume the length of the shorter piece of the rope is x meters.

According to the given information, the longer piece of the rope is equal to 5 meters longer than 4 times the shorter piece.

So, the length of the longer piece would be 4x + 5 meters.

Now, we know that the total length of the rope is 10 meters.

Therefore, we can set up an equation to solve for x:

x + (4x + 5) = 10

Simplifying the equation gives us:

5x + 5 = 10

Subtracting 5 from both sides, we get:

5x = 5

Dividing both sides by 5, we get:

x = 1

Now that we know the value of x, we can find the lengths of both sides:

Shorter piece: x = 1 meter

Longer piece: 4x + 5 = 4(1) + 5 = 4 + 5 = 9 meters

So, the shorter piece is 1 meter and the longer piece is 9 meters.

Let's assume that the shorter piece of the rope has a length of x meters.

According to the problem, the longer piece of rope is equal to 5 meters longer than 4 times the shorter piece.

So, the longer piece can be expressed as (4x + 5) meters.

Now, we know that the sum of the lengths of the shorter and longer pieces should equal the length of the entire rope, which is 10 meters.

Therefore, we can write the equation:
x + (4x + 5) = 10

Simplifying the equation:
5x + 5 = 10

Subtracting 5 from both sides:
5x = 5

Dividing both sides by 5:
x = 1

So, the shorter piece of the rope has a length of 1 meter.

Now, we can find the length of the longer piece by substituting the value of x back into the expression we derived earlier.

The longer piece = 4x + 5 = 4(1) + 5 = 4 + 5 = 9

Therefore, the lengths of the two pieces are 1 meter and 9 meters, respectively.