If 20 lb of rice and 10 lb of potatoes cost 14.20$, and 30 lb of rice and 12 lb of potatoes cost 20.04$, how much will 10 lb of rice and 50 lb of potatoes cost?

Answer 1

*I assume there is a type and the cost of 30 lb of rice and 12 lb of potatoes cost $20.40 as this allows you to solve the set of equations.*

R = Price of Rice

P = Price of Potatoes

R(20) + P(10) = 14.20

R(30) + P(12) = 20.40

Multiply the both sides of the top equation by (-3) and both sides of bottom equation by 2:

R(-60) + P(-30) = -42.60

R(60) + P(24) = 40.80

Add the two equations, R will cancel out and you can solve for P:

P(-6) = -1.8 ----> Divide both sides by -6

P = $0.30

Plug this value into either of the equations and solve for R:

R(20) + 0.3(10) = 14.20

R(20) + 3.00 = 14.20

R(20) = 11.20

R = $0.56

Double check your work by putting both R and P into each equation and checking to see if they still are true:

0.56(20) + 0.30(10) = 14.20 ---> TRUE

0.56(30) + 0.30(12) = 20.40 ---> TRUE

Finally, enter these values into the question:

R(10) + P(50) =

0.56(10) + 0.30(50) = $20.60

$20.60 is the solution