If 2x + 1, x + 2, 2 and 5 are in proportion, then what is the mean proportional between 3.5(1 - x) and 8(1 + x)?

5.25

Given that 2x + 1, x + 2, 2 and 5 are in proportion,

Product of the middle terms = Product of the extreme terms 

2(x +2) = 5(2x + 1)

2x + 4 = 10x + 5

8x = -1

x = -$\frac{1}{8}$ or - 0.125

Mean proportion of a, b = $\sqrt{a\;\times\;b}$

Mean proportion of 3.5(1-x), 8(1+x) = $\sqrt{3.9375\;\times\;7}$ 

                                                     =$\sqrt{27.5625}$ = 5.25