Question

what is the least possible number which must be subtracted from 17, 23, 32 so that the resulting number are in continued proportion​

Answer 1

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Answer 2

Answer:

The least possible number is 5

Step-by-step explanation:

The given numbers are 17, 23, and 32

Let x be the least number that must be subtracted from 17, 23, and 32 so that the resulting numbers are in continued proportion.

The resulting numbers are

(17 - x), (23 - x), and (32 - x)

By using the condition of continued proportion for three numbers

(17 - x) : (23 - x) = (23 - x) : (32 -x)

$\frac{(17 -x)}{(23-x)} =\frac{(23-x)}{(32-x)}$

(17 - x) × (32 - x) = (23 - x) × (23 - x)

544 - 17x - 32x + $x^{2}$ = 529 + $x^{2}$ - 46x

15 = 3x

x = 5

The resulting numbers are given by

(17 - 5), (23 - 5), and (32 - 5)

12, 18, and 27 which are in continued proportion

Therefore the least possible number is 5