Question

Which number should be subtarcte d by 5, 19 ,16 such that resultant is in continued proportion

Answer 1

Answer:

Let x be subtracted,

so

5 - x, 19 - x, 19 - x, 16 - x are in proportion

therefore,

$\frac{5 - x}{19 - x} = \frac{19 - x}{16 - x} \\ {(19 - x)}^{2} = (5 - x)(16 - x) \\ 361 + {x}^{2} - 38x = 80 - 5x - 16x + {x}^{2} \\ 361 - 38x = 80 - 21x \\ 17x = 281 \\ x = \frac{281}{17}$