a 260 m wire is cut into 3 pieces. The second is 4 times longer than the 1st. The third is 2 times longer than the 2nd how long is each piece=
20
Let's denote the length of the first piece as x.
According to the problem, the second piece is 4 times longer than the first piece, so its length would be 4x.
Similarly, the third piece is 2 times longer than the second piece, so its length would be 2(4x) = 8x.
Now, we know that the sum of the lengths of all three pieces is equal to 260 m. Therefore, we can set up the following equation:
x + 4x + 8x = 260
Combining like terms, we get:
13x = 260
To solve for x, we need to divide both sides of the equation by 13:
x = 260 / 13
Simplifying, we find:
x = 20
Now, we can substitute this value back into the equation to find the lengths of the three pieces:
First piece: x = 20 m
Second piece: 4x = 4 * 20 = 80 m
Third piece: 8x = 8 * 20 = 160 m
Therefore, the three pieces have lengths of 20 m, 80 m, and 160 m, respectively.
To solve this problem, we can use algebraic expressions to represent the lengths of the pieces.
Let's say the length of the first piece is x meters.
According to the problem, the second piece is 4 times longer than the first piece. Therefore, its length can be represented as 4x.
Similarly, the third piece is 2 times longer than the second piece. So, its length can be represented as 2(4x) = 8x.
Now, according to the problem, the total length of the wire is 260 meters. We can write this as an equation:
x + 4x + 8x = 260
Simplifying the equation further:
13x = 260
Dividing both sides of the equation by 13:
x = 20
So, the length of the first piece (x) is 20 meters. The second piece is 4 times longer, which makes it 4x = 4 * 20 = 80 meters. The third piece is 8 times longer than the first piece, so it is 8x = 8 * 20 = 160 meters.
Therefore, the lengths of the three pieces are:
1st piece = 20 meters
2nd piece = 80 meters
3rd piece = 160 meters.
Let x = the length of the first piece.
x + 4x + (2 * 4x) = 260
5x + 8x = 260
13x = 260
x = ?