The 24 Coins

3)  There are 24 coins that total $2.90 -- nickels, dimes, and
quarters.  There are 4 more dimes than quarters.  How many of
each of  these coins is there?    
 
    25x + 10(x + 4) + 5(20 -2x) = 290
 
    25x + 10x  +40 + 100 -10x = 290
    
    25x + 140 = 290
    
    25x = 150
 
    x =  6
 
    Since "x" is 6, then there are 6 quarters, (6 + 4) dimes,
and (20-12) nickels.
 
    1.50 (6 quarters)
    1.00 (10 dimes)
    0.40 (8 nickels)
   -------------------------
    2.90 (24 coins)
 
    As you can see in the formula above, the term for the dime
takes the number value of "x" and adds 4 to it (since there are
4 more dimes than nickels).  The term for the nickel includes
"20-2x."  Though there are 24 coins, we subtract the 4 that are
being "reserved" for the dimes, to come up with this number in
the formula.  The "-2x" will then deduct the amount of the quarters
and dimes from the nickels.