Question

Divide 20 into two parts so that the sum of their reciprocals is 4/15

Answer 1

Hi ,

Change the given word problem into algebraic equation.

20 is divided into two parts.

let first part = x

second part = 20 - x

sum of their  reciprocals the two parts = 4 / 15

⇒1 / x  + 1 / ( 20 - x ) = 4 /15

⇒ [ (20 - x ) + x ] / x( 20 - x ) = 4 / 15

⇒ ( 20 ) / ( 20x - x² ) = 4/ 15

⇒ 20 × ( 15 / 4 )  = ( 20x  - x² )

⇒ 5 × 15 = 20x - x²

⇒75 = 20x - x²

⇒ x² -20x + 75 =0

⇒ x² - 5x - 15x + 75 =0

⇒ x ( x - 5 ) - 15 ( x - 5 ) =0

⇒ ( x - 5 ) ( x - 15 ) =0

∴ x - 5 = 0 or x - 15 =0

     x = 5 or x = 15  

therefore required two parts are  x and 20 -x ,
 
if x=5 then 20 -x = 20 - 5 = 15

if x= 15 then 20 -x = 20 - 15 = 5

( 5 , 15 )  or ( 15 , 5 )

I hope this helps you.

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