A180 ft long board is cut into 3 pieces. the second piece of board is twice as long as the first. the third piece of board is six times as long as the first. what is the length of the first piece of the board?

Here we can see that there has to be a single unknown variable and using that variable we have to create an equation. That equation will ultimately help us to find the exact value of the variable. This way we can easily reach the answer that is asked in the question.
Let us assume the length of the first piece = x
Length of the second piece = 2x
Length of the third piece = 6x
Now we can get to the equation
x + 2x + 6x = 180
9x = 180
x = 180/9
  = 20
So the length of the first piece of the board is 20 feet.I hope i have explained the problem to your satisfaction and understanding.
 

If a 180ft board is cut into 3 pieces, then x+y+z=180. where y=2x and z=6x. This is all given to us, and i used the variables x,y, and z to represent the three pieces. To solve this we can use substitution to solve for the length of the first board. since we know that y=2x and z=6x, then we can plug those into the equation x+y+z=180. when we do this, we get x+2x+6x=180. Now we can combine like terms to get 9x=180. now we divide each side by 9 to get x=20, so the length of the first piece of the board would be 20 feet (don't forget to label) 

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