Reciprocals??

Question

The sum of seven times the reciprocal of a number and 5/8 is 3/2. Find the number.

Answer 1

let x = number

 

reciprocal of number = 1/x

 

equation → 7(1/x) + 5/8 = 3/2

 

                      7/x + 5/8 = 3/2        in this equation the lowest common denominator = 8x.  multiply everything by 8x

 

          8x(7/x) + 8x(5/8) = 8x(3/2)  simplify

 

                          56 + 5x = 12x

                                 -5x    -5x

 

                                   56 = 7x       divide both sides by 7

 

                                  56/7 = (7x)/7   simplify

 

                                       8 = x      reciprocal would be 1/8

 

CHECK

 

7(1/8) + 5/8 = 3/2

 

7/8 + 5/8 = 3/2

 

      12/8  = 3/2

 

       3/2 = 3/2     √