If x is subtracted from each of the numbers 20, 37, 54 and 105, then the numbers so obtained in this order are in proportion. What is the mean proportional between (7x - 5) and (x + 1)?
Answer & explanation
Correct answer: option 1
The proportion :
(20 - x) : (37 - x) :: (54 - x) : (105 - x)
Product of middle terms = Product of extreme terms
(37 - x)(54 - x) = (20 - x)(105 - x)
1998 - 91x + x² = 2100 - 125x + x²
34x = 102
x = 3
7x - 5 = 16, x + 1 = 4
Mean proportion to a, b = $\sqrt{a\; \times\; b}$
Mean proportion of 19, 4 = $\sqrt{16\; \times\; 4}$
= 8