Question 10153
D is dimes,Q is quarters, H is half dollars

 We have D + Q + H = 24
   D = Q + 5

 The value of the coins is 

 10D + 25Q + 50H = 545

 By the first two equations

 2Q +5 + H = 24

 1)        2Q + H = 19   

 By the second and third equations

 10(Q+5) + 25Q + 50H = 545

  This can be reduced to 

 2)         7Q + 10H = 99   

 Solve 1) and 2) for Q 
 Q = 7

 Then D = Q + 5

        = 12

 By 1)   H = 19 - 2Q
            = 5

 Twelve dimes in purse