Question

The number obtained by subtracting 6 from a positive number is 27 times the inverse of the original number. What is the original number

Answer 1

Answer: 9

Step-by-step explanation:

Let the original number be a

ATQ

a - 6 = 27 x 1/a

a - 6 = 27/a

a(a - 6) = 27

a^2 - 6a - 27 = 0

Applying middle term Facorisation

a^2 - 9a + 3a - 27 = 0

a(a - 9) + 3(a - 9) = 0

Either

a + 3 = 0

a = -3 {a cannot be -3 since the required number is positive}

So

a - 9 = 0

a = 9

Thus the required number is 9

Verification

a - 6 = 27 x 1/a

9 - 6 = 27 x 1/9

3 = 3

LHS = RHS

Hence verified