Question

Divide 50 into two parts such that the sum of their reciprocals is 1/12. the numbers are

Answer 1

Let one number be x

the other number will be 50-x  

1/x + 1/(50-x)= 1/12  

50-x+x = x(50-x)/12  

 

600 = 50x-x^2  

x^2-50x+600=0  

x^2-30x-20x+600=0  

x(x-30)-20(x-30)=0  

(x-30)(x-20)=0  

x= 20 or 30

the numbers are 20 and 30