You obviously can't have any pennies, because you couldn't have 1-4 pennies,
since $1.15 is a multiple of 5, and if you had 5 pennies or more you could
change a nickel. 

You can't have more than 1 nickel, otherwise you could change a dime.
And if you had 1 nickel you couldn't have but 1 dime, otherwise you could
change a quarter.  Then if you had 1 nickel and 1 dime you'd have 15 cents.
That would leave $1.00 and you couldn't make that remaining $1.00 with quarters
and halves without either being able to change a half or a dollar.

So you can't have any pennies or nickels.

Since you can't have any pennies or nickels, you can't possibly make $1.15 with
dimes and halves only, so you must have at least 1 quarter.  You can't have
more that one quarter, otherwise you could change a half. So you must have
exactly 1 quarter. 

That leaves 90 cents, to make with a half dollar and dimes.  So that's 1
half and 4 dimes. And with only 4 dimes you can't change a half dollar.

So that's the answer:  4 dimes, a quarter and a half dollar.    

Edwin