SOLUTION: the tollboth is 50 cents for eash car how many diffrent ways can you use quarters, dimes, and nickels

We just need to think about the quarters and dimes for the rest can
always be made up with nickels.  There are three cases, using
0,1, and 2 quarters:

1.  If you don't use any quarters, then you can use 0 dimes
up through 5 dimes, (and the rest, if any, in nickels).  
That's 6 ways.

2. If you use 1 quarter, you can use 0 dimes up through 2 dimes,
(and the rest in nickels).  That's 3 more ways.

3. If you use 2 quarters, that's the whole 50 cents, so that's 1 more way.

So that's 6+3+1 or 10 ways. 

 1. 0 quarters, 0 dimes, 10 nickels.
 2. 0 quarters, 1 dime,   8 nickels.
 3. 0 quarters, 2 dimes,  6 nickels.
 4. 0 quarters, 3 dimes,  4 nickels.
 5. 0 quarters, 4 dimes,  2 nickels.
 6. 0 quarters, 5 dimes,  0 nickels.
 7. 1 quarter,  0 dimes,  5 nickels.
 8. 1 quarter,  1 dime,   3 nickels.
 9. 1 quarter,  2 dimes,  1 nickel.
10. 2 quarters, 0 dimes,  0 nickels.

Edwin