A 25-foot board is to be cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is one foot more than five times the length of the first piece. What are the lengths of the three pieces?

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Answer 1 · 2016-06-27T03:12:09

Length of the 3 pieces are #3, 6, 16#

Assume the length of the first, second and third pieces to be #p_1, p_2, p_3# respectively

Given from the problem:

#p_1+ p_2 + p_3 = 25# -> Equation 1

#p_2 = 2 p_1#

#p_3 = 5 p_1 + 1#

Substituting the values of #p_2, p_3# in equation 1, we get

#p_1+ 2 p_1 + (5 p_1 + 1) = 25#

#8p_1+ 1 = 25# => #8p_1 = 24# => #p_1 = 3#

Hence, #p_2 = 2*3# => #p_2 = 6 # and #p_3 = 5*3 + 1# => # p_3=16#