Expert: Sherman D. - 12/8/2004

Question
(Word Problem)

A rope that is 344 ft long is to be cut into three pieces such that the second piece is 6 ft shorter than three times the first and the third is 2 ft longer than two-thirds of the second. Find the length of the longest piece.";  

Answer
x + y + z = 344

y = 3x - 6
z = (2/3)y + 2

z = (2/3)(3x - 6) + 2
z = (6/3)x - (12/3) + 2
z = 2x - 4 + 2
z = 2x - 2

x = x
y = 3x - 6
z = 2x - 2

x + (3x - 6) + (2x - 2) = 344
x + 3x - 6 + 2x - 2 = 344
6x - 8 = 344
6x = 352
x = 58 2/3

y = 3(58 2/3) - 6
y = 3(176/3) - 6
y = 176 - 6
y = 170

z = (2/3)(170) + 2
z = (340/3) + 2
z = (340/3) + (6/3)
z = (346/3)
z = 115 1/3

The longest length is 170 ft.