Bethany has 3.10$ in nickels and dimes. she has a total of 44 coins . what is the value of the nickels bethany has

Represent the unknows with n and d.

Then n+d = 44 (# of coins)

and 

$0.05n + $0.10d = $3.10   (value of coins)

Solving the first equation for n, we get n = 44-d.  Subst.  44-d for n in the 2nd equation:

0.05(44-d) + 0.10d = 3.10
Then 2.20 - 0.05d + 0.10d = 3.10, or
          2.20 + 0.05d             = 3.10, or    0.05d = 0.90.  Solving for d, 
       0.90
d = = 18
        0.05

There are 18 dimes and 44-18 nickels.  How many nickels is that?  ;)