Question 451513
Let's mark:

  q - number of quarters Sandy has
  n - number of nickels  Sandy has

Number of coins Sandy has is 

  q + n = 41

Everything has to be in the same units so $7.05 = 705 cents
Value of coins Sandy has is

  25*q + 5*n = 705

We have two equations with two variables

    q +   n = 41, let express q as q = 41 - n
 25*q + 5*n = 705

 25*(41-n) + 5*n = 705    , replace q with expression from above
 1025 - 25*n + 5*n = 705  , multiply 
 1025 - 705 = 25*n - 5*n  , move unknowns to one and numbers to other side
 320 = 20*n               , combine variables and numbers on each side
 n = 320/20               , invert multiplication

 n = 16, number of nickles Sandy has

 q = 41 - 16              , replace n witht he found value
 q = 25, number of quarters Sandy has

check: 25*25 + 5*16 = 625 + 80 = 705, OK