Question 948389
To solve this problem, we have to find out how many dimes and nickels constitute the value of $4.10. I believe the simplest way of doing this is by creating two separate equations. In this problem:

x = amount of nickels 
y = amount of dimes 

Thus, the two equations will be:
x + y = 51 
0.05x + 0.10y = 4.10 

Let's solve for x. To do this, multiple the bottom equation by 20, so that the x on the top equation will cancel out with the x on the bottom equation after subtraction: 
x + y = 51
x + 2y = 82 

Reverse the equation for logical standards:
x + 2y = 82 
x + y = 51

Now, subtract the bottom from the top (the x's cancel out):
y = 31 

Thus, there are 31 dimes. Since there are 51 total coins, there will be 20 (51-31) nickels.

31-20 = 11

Therefore, there are 11 more dimes than nickels.