Word Problem

Question

How many pounds of nuts selling for $12 per lb and raisins selling for $6 per lb should a person combine to obtain 120 lb of a trail mix selling for $8 per lb? The person would need
( ) lb of nuts selling for $12 and
( )lb of raisins selling for $6.

Answer 1

 

Let N = number of pounds of nuts

Let R = number of pounds of raisins

 

We can construct the following system of equations:

 

   12N + 6R = 8(120)

 

   N + R = 120

 

Solving for N in the second equation, we have:

 

   N = 120 - R

 

Substituting that into equation 1, we have:

 

   12(120 - R) + 6R = 8(120)

 

   1440 - 12R + 6R = 960

 

   1440 - 6R = 960

 

   1440 - 960 = 6R

 

   480 = 6R

 

   R = 80

 

We need 80 pounds of raisins.

We need 40 pounds of nuts.