We can't do it using just 1 quarter because then we'd have
to have the remaining 70 cents with 6 coins, and 6 dimes is
only 60 cents.  So we can't use just one quarter.

If we use just 2 quarters, we have to have the remaining 
45 cents with 5 coins, which we can have with 4 dimes and 
1 nickel. That's the only way with 2 quarters.  So one way is

1.   2 quarters, 4 dimes, and 1 nickel.

If we use 3 quarters, we have to have the remaining 
20 cents with 4 coins, which we can have with 4 nickels. 
That's the only way with 3 quarters.  So a second way is

2.   3 quarters and 4 nickels.

Half dollars (50 cent pieces) are not in circulation, but
if we can use 1 half dollar, then we have to have the remaining 
45 cents with 6 coins.  The only way we can have that is with
3 dimes and 3 nickels.  So a third way is

3.   1 half dollar, 3 dimes, and 3 nickels.

So there are three ways, if your teacher allows you to use a
half dollar.  Otherwise there are only 2 ways.

Edwin