If $30 \mathrm{lb}$ of rice and $30 \mathrm{lb}$ of potatoes cost $\$ 30.60$, and $20 \mathrm{lb}$ of rice and $12 \mathrm{lb}$ of potatoes cost $\$ 17.04$, how much will $10 \mathrm{lb}$ of rice and 50 lb of potatoes cost?

Let $x$ be the cost of $1 \mathrm{lb}$ of rice and $y$ be the cost of $1 \mathrm{lb}$ of potatoes. Set up two linear equations from the given information using $x$ and $y$ as the variables.
\[
\begin{array}{l}
\square=30.60 \\
\square=17.04
\end{array}
\]

Step 1 ：Let's denote the cost of 1 lb of rice as \(x\) and the cost of 1 lb of potatoes as \(y\).

Step 2 ：From the given information, we can set up two equations. The first one is \(30x + 30y = 30.60\) and the second one is \(20x + 12y = 17.04\).

Step 3 ：Solving these two equations, we find that \(x = 0.60\) and \(y = 0.42\).

Step 4 ：Now, we can calculate the cost of 10 lb of rice and 50 lb of potatoes by multiplying the cost of 1 lb of each item by the respective quantities. This gives us \(10x + 50y\).

Step 5 ：Substituting the values of \(x\) and \(y\) into the equation, we get \(10*0.60 + 50*0.42 = 27.00\).

Step 6 ：Final Answer: The cost of 10 lb of rice and 50 lb of potatoes is \(\boxed{27.00}\).