I won't tell my wealth!

Let's say that Mrs. Parker has $n$ nickles and $q$ quarters. From the second sentence we know that $6 | n, 5 | q$ so we may write $n = 6x, q = 5y$ . From the third sentence we know that the linear diophantine equation $n+q = 120$ holds so we have $6x + 5y = 120$ . This equation implies that $5y \equiv 0 \mod 6 \implies y \equiv 0 \mod 6 \implies y = 6y'$ and $6x \equiv 0 \mod 5 \implies x \equiv 0 \mod 5 \implies x = 5x'$ so in our new variables the equation becomes $30x' + 30y' = 120$ which then implies $x' + y' = 4$ . We also know that both variables have to be positive, leaving only the solutions $(x'=1, y'= 3),(x'=2,y'=2),(x'=3,y'=1)$ .

The value of the coins Mrs. Parker has must be $0.05n + 0.25q = 0.3x + 1.25y = 1.5x' + 7.5y'$ . If we substitute the solutions for $x',y'$ we find that all the values listed, except for $15\$$ are possible.