A newspaper reported that candidate Williams received 13500

A newspaper reported that candidate Williams received 13,500 more votes that her opponent Ms. Smith, and that 42,310 votes were cast in the election. How many votes were cast for each candidate?

Solution

Let W and S stand for the votes cast for WIlliams and Ms.Smith

Given

                             W+S= 42310..................(1)

and

                             W-S = 13500..................(2)

Adding (1) and (2)   2W= 55810

                   So            W= 27905 and

                                    S = 42310-27905

                                       =14405

So votes cast for Williams and MsSmith are 27905 and 14405 respectively.