If 20 lb of rice and 10 lb of potatoes cost $10.20, and 30 lb of rice and 12 lb of potatoes cost $14.04, how much will 10 lb of rice and 50 lb of potatoes cost?

We are going to set up a system of equations to solve for how much 1 pound of each costs then find how much 10 lbs of rice + 50 lbs of potatoes cost. 

Let a = rice, b = potatos

20a + 10b = 10.20
30a + 12b = 14.04

I'm going to multiply the first equation by 3 and the second equation by - 2.

60a + 30b = 30.60
- 60a - 24b = 28.08

Notice the a-variables will cancel. Combine like terms and constants and solve for b.

6b = 2.52
b = 0.42

Now we plug in our answer for b and solve for a. 

20a + 10(0.42) = 10.20
20a + 4.20 = 10.20
20a = 6
a = 0.30

So 1 lb of rice is 30 cents and 1 lb of potatoes is 42 cents. 

Now we do 10a + 50b.

10(0.30) + 50(0.42)
3 + 21 
24. 

10 lbs of rice and 50 lbs of potatoes would cost $24.