solution: Let the number of dimes Hillary has be $d$ and the number of nickels she has be $n$. We have the two equations \begin{align*}
  d+n&=11\\
  10d+5n&=75
  \end{align*} (The last equation is in terms of cents.) To make the second equation nicer, we divide both sides by 5 to get $2d+n=15$. From the first given equation, we have $d=11-n$. Substituting this into the simplified second given equation to eliminate $d$, we get $2(11-n)+n=15\Rightarrow n=7$. Thus, Hillary has $\boxed{7}$ nickels.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Hillary has eleven coins, all dimes and nickels. In total, the coins are worth 75 cents. How many nickels does she have?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 7
extra_info.question: Hillary has eleven coins, all dimes and nickels. In total, the coins are worth 75 cents. How many nickels does she have?
extra_info.split: test