Question 761831
x = dimes
y = quarters
  x +   y = 37...1
10x + 25y = 550..2
Multiply (1) by 10
10x + 10y = 370...3
10x + 25y  = 550...2
subtract (3) from (2)
      15y  = 180
       y   = 12
Substitute y = 12 into (1)
  x  +  y  = 37
  x  +  12 = 37
         x = 37 - 12
         x = 25
So, there are 25 dimes + 12 quarters.
Hope this helps.
:-)