SOLUTION: an 18 ft pipe is to be cut into 3 pieces such that the second piece is 1 foot longer than the first, and the third piece is 1 foot longer than the second. what is the longest piece

Question 322604: an 18 ft pipe is to be cut into 3 pieces such that the second piece is 1 foot longer than the first, and the third piece is 1 foot longer than the second. what is the longest piece?
Answer by jessica43(140) (Show Source): You can put this solution on YOUR website!
The trick here is to change this word problem into 3 separate equations.
First you know that 3 pieces of pipe will add up to 18 ft. This can be written as an equation:
A + B + C = 18
Next, you know that piece B is 1 ft longer than piece A:
B = A + 1 (or can also be written as A = B - 1)
Finally, you know that piece C is 1 ft longer than piece B:
C = B + 1 (or B = C - 1)
Now we want to combine all three equations. We need to plug the second and third equations into the first and make sure there is only one variable to solve for. Since B is in all three equations, let that be our variable. So we plug A = B - 1 and C = B + 1 into equation one:
A + B + C = 18
(B-1) + B + (B+1) = 18
3B - 1 + 1 = 18
3B = 18
B = 6
Now you can plug B into equations 2 and 3 to solve for A and C:
A = B - 1
A = 6 - 1
A = 5
C = B + 1
C = 6 + 1
C = 7
So piece C (the third piece) is your longest piece at 7 ft.
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