Question 371773
nickels = .05
dimes = .10
quarters = .25

Let x = number of nickels
Let y = number of dimes
Let z = number of quarters

.10y + .25z = 7.85
.05x + .25z = 6.35
.05x + .10y = 4.70

Using the elimination method: 
.10y + .25z = 7.85
-(.05x + .25z = 6.35)

Thus -.05x + .10y = 1.50
Now add:
 -.05x + .10y = 1.50
  .05x + .10y = 4.70
Thus .20y = 6.20
y = 31

Substitute y into .05x + .10y = 4.70
.05x + .10(31) = 4.70
.05x + 3.10 = 4.70
.05x = 1.60
x = 33

Substitute x into .05x + .25z = 6.35
.05(33) + .25z = 6.35
1.60 + .25z = 6.35
.25z = 4.75
z = 19

Therefore, x=33 (nickels), y=31 (dimes), z=19 (quarters)

Double Check:  
.10y + .25z = 7.85
.10(31) + .25(19) =?= 7.85
3.10 + 4.75 =?= 7.85
7.85 = 7.85 Correct!