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A 100-foot rope is cut into three pieces. The first piece is three times as long as the second, and the third piece is \(40\) feet shorter than the second. How many feet long is the shortest piece?

 May 17, 2022
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Let the length of the 2nd piece ==L

Then, the length of the 1st piece==3L

The length of the shortest piece ==3L - 40

 

[L + 3L + 3L  -  40] ==100, solve for L

7L ==100  +  40

7L ==140

 

L ==140 / 5 ==20 feet - length of the 2nd piece

20  x  3 ==60 feet - length of the 1st piece.

60 - 40 ==20 feet - length of the 3rd piece.

 

Note: The 3rd piece must be 40 feet shorter than the FIRST and NOT the SECOND piece.

 May 17, 2022

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