if 20lbs of rice and 10lbs of potatoes cost $16.20, and 30lbs of rice and 12lbs of potatoes cost 23.04, how much will 10lbs of rice and 50lbs of potatoes cost?

Question

need help converting the word problem into an equation and solving it.

Answer 1

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.