The shorter piece is 15 feet, while the longer piece is 25 feet
Let the longer piece be y, and the shorter piece be x.
So, we have:
[tex]x + y = 40[/tex] --- the length of the rope
[tex]y =2x - 5[/tex] --- the relationship between the short and the long piece
Substitute 2x - 5 for y in [tex]x + y = 40[/tex]
[tex]x + 2x - 5 =40[/tex]
[tex]3x - 5 =40[/tex]
Add 5 to both sides
[tex]3x =45[/tex]
Divide both sides by 3
[tex]x =15[/tex]
Substitute 15 for x in [tex]y =2x - 5[/tex]
[tex]y =2 \times 15 -5[/tex]
[tex]y =30 -5[/tex]
[tex]y =25[/tex]
Hence, the shorter piece is 15 feet, while the longer piece is 25 feet
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