Let r=unit price of rice in $/lb and p=unit price of potatoes, then
20r+10p=16.20 and 30r+12p=23.04.
So 2r+p=1.62 and p=1.62-2r.
2.5r+p=1.92, so p=1.92-2.5r.
Therefore 1.62-2r=1.92-2.5r.
0.5r=0.3 so r=$0.60 /lb. Also, p=1.62-2r=1.62-1.20=$0.42 /lb.
Therefore 10r+50p=6+21=$27.