Mrs. clause has five less dimes than nickels in her red purse that total $3.10. how many each type of coin does she have? write out the equation.

Let d = number of dimes and n = number of nickel.
We can now set up the following system of equations:_

10d + 5n = 310(1)
n - d = 5
multiply second equation by -5:-
-5n + 5d = -25(3)

Adding  (1) and (3)  gives:_

 15d = 285

d = 19   and so n = 19+5 = 24 

So she has 19 dimes and 24 nickels   Answer