Question

Form linear equations to represent the given situation. -
The sum of two numbers is 16 and the sum of their reciprocals is,​

Answer 1

Answer:

Let one number be x.

therefore , another number = 16 - x  

      (because sum of two numbers is 16)

also ,

      1/x + 1/16 - x  = 1/3 (Given)

  16 -x +x / x(16 -x) = 1/3

  16*3 = x(16 - x)

  48 = 16x - x²

or x² - 16x + 48 = 0

or x² - 12x - 4x + 48 =0

x(x-12) -4(x-12) =0

x-4 = 0 or x-12 =0

x=4 or x=12

hence one Number is 4 .

and another number = 16 - x =16 - 4 = 12 .

Step-by-step explanation: