SOLUTION: A coin bank contains coins in dimes and quarters with a total value of $23.70. There are eight fewer dimes than quarters. Find the number of dimes in the bank.

   Q -  D   =    8      (1)    (counting coins)
25*Q + 10*D = 2370      (2)    (counting cents)


==========================>  Divide eq(2) by 5; Multiply eq(1) by 2. You will get

  2Q - 2D =  16         (3)
  5Q + 2D = 474         (4)
------------------------------Add eq(3) and eq(4)
  7Q = 490

  ========================>  Q =  = 70.


Answer.  70 quarters and 70-8 = 62 dimes.


Check.   The total is  70*25 + 62*10 = 2370 cents.   ! Correct !

Put aside 8 quarters of your collection.
Then the updated collection is worth 2370 - 8*25 = 2170 cents.

But this time it consists of equal number of quarters and dimes,
and yoU can group quarters and dimes in groups (sets) in a way that each group/set contains exactly one quarter and one dime.


Thus each group is worth 25 + 10 = 35 cents,  and the number od such groups is

 = . = 31*2 = 62 groups.


Should I explain further that you have 62 dimes and 62+8 = 70 quarters ??


The same answer. But  MENTAL  solution.