Question 375813: a 25 inch pieace of board is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is one inch more than five times the lenght of the first piece. If x represents the first piece what is the length of all three pieces?
Answer by jessica43(140)   (Show Source):
You can put this solution on YOUR website! To solve this equation, you are going to have to write 3 separate equations using what you know.
First, you know that a 25 inch board is cut into 3 pieces:
x + y + z = 25 (where x = first piece, y = second piece, z = third piece)
Second, you know that the second piece is twice as long as the first piece:
y = 2x
Third, you know that the third piece is one inch more than five times the length of the first piece:
z = 1 + 5x
Now that we have our three equations, we see that both y and z can be rewritten in terms of x. That means we can plug the second and third equations into the first equation and solve for x:
x + y + z = 25
x + (2x) + (1 + 5x) = 25
8x + 1 = 25
8x = 24
x = 3
Now plug this into the second and third equations to find the values for y and z:
y = 2x
y = 2(3)
y = 6
z = 1 + 5x
z = 1 + 5(3)
z = 16
So the first piece is 3 inches, the second is 6 inches and the third is 16 inches.
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