42inch board is cut into 3peices. Peice 2 is twice as long as the 1st & 3rd peice. Peice 3 is three times as long as peice 1. What are the lengths of all 3 peices?
Pc 1
Pc 2
Pc 3
This makes no sense. Please check for typos.
I typed it just as it was stated in the book. I figured it out. Thanx...
pc1 7inches
pc2 14inches
pc3 21inches
To solve this problem, we can set up a system of equations to represent the relationships between the lengths of the three pieces.
Let's assume the length of the first piece is x.
According to the given information, the second piece is twice as long as the first piece. So, the length of the second piece is 2x.
Similarly, the third piece is three times as long as the first piece. Therefore, the length of the third piece is 3x.
Now, we know that the sum of the lengths of all three pieces is equal to the initial length of the board, which is 42 inches.
So, we can write the equation:
x + 2x + 3x = 42
Combining like terms, we get:
6x = 42
Dividing both sides of the equation by 6, we obtain:
x = 7
Now, we can substitute this value back into the expressions for the lengths of the second and third pieces to find their values:
Second piece (Pc 2) = 2x = 2 * 7 = 14 inches
Third piece (Pc 3) = 3x = 3 * 7 = 21 inches
Therefore, the lengths of the three pieces are as follows:
Pc 1: x = 7 inches
Pc 2: 2x = 14 inches
Pc 3: 3x = 21 inches