42 inch board is cut into 3 pieces. Piece 2 is twice as long as the 1st & 3rd piece. Piece 3 is three times as long as piece 1. Find inches of all three pieces
11 years ago
11 years ago
separately
11 years ago
If piece 2 is twice piece 1, then
x = piece 1
3x = piece 3 (3 times piece 1)
2x = piece 2 (twice piece 1)
x + 3x + 2x = 42
6x = 42
x = 7
Piece 1 - 7
Piece 2 - 14
Piece 3 - 21
11 years ago
If piece 2 is twice piece 3, then
x = piece 1
3x = piece 3 (3 times piece 1)
2(3x) = piece 2 (twice piece 3)
x + 3x + 2(3x) = 42
10x = 42
x = 4.2
Piece 1 - 4.2
Piece 2 - 12.6
Piece 3 - 25.2
11 years ago
If piece 2 is twice piece 1 & 3, then
x = piece 1
3x = piece 3 (3 times piece 1)
2(3x + x) = piece 2 (twice piece 1 & 3)
x + 3x + 2(4x) = 42
12x = 42
x = 3.5
Piece 1 - 3.5
Piece 2 - 10.5
Piece 3 - 28
11 years ago
I'm confused. Shouldn't pc 2 be the largest since it says that pc2 is twice as long as pc 1&3, and pc 3/three times as long as pc1
11 months ago
To find the length of the three pieces, let's assign variables to represent the length of each piece. Let's call the length of the first piece "x".
According to the question, the second piece is twice as long as the first piece, so its length would be 2x.
The third piece is three times as long as the first piece, so its length would be 3x.
We also know that the sum of the lengths of the three pieces should equal 42 inches.
So, we can write an equation to express this as:
x + 2x + 3x = 42
Simplifying the equation, we get:
6x = 42
Dividing both sides of the equation by 6, we find:
x = 7
Now that we know the value of x, we can substitute it back into the expressions for the lengths of the three pieces:
First piece: x = 7 inches
Second piece: 2x = 2 * 7 = 14 inches
Third piece: 3x = 3 * 7 = 21 inches
Therefore, the lengths of the three pieces are:
First piece: 7 inches
Second piece: 14 inches
Third piece: 21 inches