Question 745278
1 Dime = $0.10  and 1 Quarter = $0.25

Let x - the number of dime 
y - the number of quarter

Number of coins she has: x + y = 40 coins

Now, 0.10x for dime plus 0.25y for quarter is equal to $6.85 that is,
0.10x+0.25y=6.85

Then,
Multiply -0.10 to (x + y = 40)  it becomes -0.10x -0.10y = -4, then add this to 
0.10x+0.25y=6.85 it yields y = 19 quarters and x = 21 dimes