Word problem

Question

If 20 lb of rice and 30 lb of potatoes cost $29.80, and 30 lb of rice and 12 lb of potatoes cost $29.52, how much will 10 lb of rice and 50 lb of potatoes cost?

Answer 1

Rewrite the problem as two linear equations

 

r = price of 1 lb. of rice

 

p = price of 1 lb. of potatoes

 

20r + 30p = 29.80

30r + 12p = 29.52

 

Multiply first equation by 1.5. You get:

 

30r + 45p = 44.70

30r + 12p = 29.52

 

Subtract second equation from the first one. You get:

 

33p = 15.18

   p = .46

 

Put this value for p back in the first equation. You get:

 

30r + 20.70 = 44.70

       -20.70.   -20.70

30r = 24

r = .80

 

Now we can find out what 10 lb. of rice & 50 lb. of potatoes cost by putting values for r and p in the equation.

 

10r + 50p = 10(.80) + 50(.46) = 8 + 23 = 31 dollars