Question 90786
 

     One number is 5 times another. If the sum of their reciprocals is , find the two numbers. Define the variables you use, and remember to check your solutions

          Let the variables be x & y 
           given one variable is 5 times the other , we get x = 5y.....eq'n (1)

          sum of their reciprocals = 1/5,  i.e, 1/x+1/y = 1/5........eq'n(2)

         substitute for x in eq'n(2)

                     1/5y+1/y = 1/5
                       (1+5)/5y = 1/5

                        6/5y = 1/5

                         y = 6*5/5 = 6

          substituting for y in Eq(1) we get x = 5*6 = 30

    the solution for the variables is x =30  & y=6



verification: x= 5y,     30 = 5*6,  30 = 30

            1/x+1/y = 1/5,   1/30+1/6 = 1/5,  (1+5)/30  = 1/5,  6/30 = 1/5
                                                                 1/5 = 1/5 
       hence verified