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 \(\boxed{27.00}\).