Reciprocals??

Question

The sum of four times the reciprocal of a number and 3/4 is 49/44. Find the number.

Answer 1

let x = number

 

1/x = reciprocal of number

 

equation   →     4(1/x) + 3/4 = 49/44

 

                           4/x + 3/4 = 49/44         the lowest common denominator is 44x.  multiply everything by 44x

 

           44x(4/x) + 44x(3/4) = 44x(49/44)     simplify

 

                          176 + 33x = 49x     subtract 33x from both sides

 

                                  -33x    -33x

 

                                    176 = 16x           divide both sides by 16

 

                                    176/16 = (16x)/16

 

                                           11 = x       this is the number and the reciprocal would be 1/11

 

 

 

CHECK

 

4(11) + 3/4 = 49/44

 

4/11 + 3/4 = 49/44      LCD = 44  multiply everything by 44

 

44(4/11) + 44(3/4) = 44(49/44)

 

                 16 + 33 = 49

 

                         49 = 49     √