A 36-meter rope is divided into three pieces. One piece is twice as long as the shortest piece, and the third piece is 1 meter longer than four times the shortest piece. Find the length of the shortest piece.

x + 2x + 4x+1 = 36

To solve this problem, let's assign a variable to represent the shortest piece's length.

Let's say the length of the shortest piece is "x" meters.

According to the given information, one piece is twice as long as the shortest piece. Therefore, one piece's length is 2x meters.

The third piece is 1 meter longer than four times the shortest piece. So, the third piece's length is (4x + 1) meters.

Now, we know that the sum of the lengths of all three pieces is equal to 36 meters.

So we can write the equation: x + 2x + (4x + 1) = 36

Combining like terms, we get: 7x + 1 = 36

Next, we isolate the variable by subtracting 1 from both sides of the equation: 7x = 35

To solve for x, we divide both sides of the equation by 7: x = 35/7

Simplifying the right side, we find that x = 5.

Therefore, the length of the shortest piece is 5 meters.