Question 751202
x = quarters  y = dimes

x   + y   = 54...(1)
25x + 10y = 1230 ....(2)

Multiply (1) by 10

10x + 10y = 540 ....(3)
25x + 10y = 1230....(2)

Subtract (2) from (3)

15x       =  690
  x       =  46

substitute x = 46 into Eq (1)

x + y = 54
46 + y = 54
     y = 54 - 46
     y = 8
Therefore there are 46 quarters + 8 dimes

Hope this helps
:-)