Question

what least number should be subtracted from 11 27 35 and 99 in order to get four numbers in proportion ?​

Answer 1

Step-by-step explanation:

Let us subtract x from the given numbers:

So, 11 - x, 27 - x, 35 - x, 99 - x will be in proportion. Hence,

$\frac{11 - x}{27 - x} = \frac{35 - x}{99 - x} \\ by \: invertendo \\ \frac{27 - x}{11 - x} = \frac{99 - x}{35 - x} \\ by \: dividendo \\ \frac{27 - x - (11 - x)}{11 - x} = \frac{99 - x - (35 - x)}{35 - x} \\ \frac{27 - x - 11 + x}{11 - x} = \frac{99 - x - 35 + x}{35 - x} \\ \frac{16}{11 - x} = \frac{64}{35 - x} \\ \frac{1}{11 - x} = \frac{4}{35 - x} \\ 35 - x = 4(11 - x) \\ 35 - x = 44 - 4x \\ 4x - x = 44 - 35 \\ 3x = 9 \\ x = \frac{9}{3} \\ x = 3 \\ so \: \\ 11 - x = 11 - 3 = 8 \\ 27 - x = 27 - 3 = 24 \\ 35 - x = 35 - 3 = 32 \\ 99 - x = 99 - 3 = 96 \\ hence \: 8, \: 24, \: 32, \: 96 \: are \: in \: proportion.$