A pen and its ink refill together cost $\;\$1.10$. The pen costs $\;\$1$ more than the ink refill. What is the cost of the pen in dollars?
Begin by assigning variables.  Let $p$=the cost of the pen and $i$=the cost of the ink.  From what we are given,
\begin{align*}
p+i&=1.10,\\
p&=1+i.
\end{align*} Substituting for $p$ in the first equation, we find: $1+i+i=1.10$, so $2i=.10$ and $i=.05$. Therefore, $p=1+i=\boxed{1.05}$ dollars.
1.05
Level 2
Algebra
Problem: A pen and its ink refill together cost $\;\$1.10$. The pen costs $\;\$1$ more than the ink refill. What is the cost of the pen in dollars?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>Let the cost of the ink refill be denoted as x dollars. Since the pen costs $1 more than the ink refill, the cost of the pen can be expressed as x + 1 dollars. The total cost of the pen and the ink refill together is given as $1.10. Therefore, we can set up the following equation:

x + (x + 1) = 1.10

This simplifies to:

2x + 1 = 1.10

Next, we isolate the variable x by subtracting 1 from both sides:

2x = 1.10 - 1
2x = 0.10

Now, we divide both sides by 2 to solve for x:

x = 0.10 / 2
x = 0.05

This means the cost of the ink refill is $0.05. To find the cost of the pen, we substitute x back into the expression for the pen's cost:

Cost of the pen = x + 1
Cost of the pen = 0.05 + 1
Cost of the pen = 1.05

Thus, the final answer is $1.05.<|END_OF_LATENT|> The final answer is $1.05$.