SOLUTION: A 29-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is two inches more than six times the length of

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Question 1208338: A 29-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is two inches more than six times the length of the first piece. Find the lengths of the pieces.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Answers:
1st piece = 3 inches
2nd piece = 6 inches
3rd piece = 20 inches


Work Shown

x = length of 1st piece
2x = length of 2nd piece
6x+2 = length of 3rd piece

(1st)+(2nd)+(3rd) = total
(x)+(2x)+(6x+2) = 29
9x+2 = 29
9x = 29-2
9x = 27
x = 27/9
x = 3 inches is the length of the 1st piece.
2x = 2*3 = 6 inches is the length of the 2nd piece.
6x+2 = 6*3+2 = 18+2 = 20 inches is the length of the 3rd piece.

Check:
1st+2nd+3rd = 3+6+20 = 29
The answers are confirmed.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

It can be easily solved mentally.


For a moment, take away these two extra inches. 

Then you will have three pieces of x, 2x and 6x inches with the total of 29-2 = 27 inches.


So,  x + 2x + 6x = 27,

     9x = 27

      x = 27/9 = 3.


Thus, in the modified problem, the pieces are 3 inches, 6 inches and 18 inches.


Now return two inches to the 18 inches piece to get the true value of 18+2 = 20 inches.


So, your answer is 3 in, 6 in and 20 in.


This entire reasoning can be done in the head in 30 seconds without paper writing.


Develop your mental skills this way.  This problem fits very well for it.

Solved.



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