Solving linear

Question

A rope that is 168ft long is to be cut inti three pieces such that the second piece is 6ft less than three times the first, and the third is 2ft more than two-thirds of the second. Find the length of the longest 

Answer 1

1st piece = x

 

2nd piece 3x-6

 

3rd piece 2/3(3x-6) + 2

             2x - 4+2 =

             2x-2

 

168 = x + 3x-6 + 2x - 2 = 6x - 8

 

176 = 6x

 

88 = 3x

 

x = 88/3 = 29 1/3

 

1st: 88/3

2nd :   3(88/3) - 6 = 82

3rd: 2*88/3 - 2 = 176/3 - 6/3 = 170/3 = 56 2/3