Applications 1.2

Question

The manager of Nut's Nuts regularly sells cashews for $6.50 per pound, pecans for $7.50 per puns, and peanuts for $2.00 per pound. How many pounds of cashews and pecans should be mixed with 40 pounds of peanuts to obtain a mixture of 100 pounds that will sell for $4.89 a pound so that the revenue is unchanged?

Answer 1

Ariel:

 

Let C pounds of cashews and P pounds of pecans be mixed with 40 pounds of peanuts.  The mixture is to be of 100 pounds. So

 

C + P + 40 = 100, that is C + P = 60, that is C = 60 - P.

 

This mixture is going to be sold for $4.89/pound.  So the revenue is going to be 100 x 4.89 = $489.

 

Revenue from cashews alone is (6.50) C.  Revenue from pecans alone is (7.50) P and revenue from peanuts alone is (2.00) (40).  The total  revenue from separate sales is (6.50)C + (7.50)P + (2.00) (40).

 

If the revenue from the mixture is the same as that from separate sales, we have

 

(6.50)C + (7.50)P + (2.00) (40) = 489, that is, (6.5)C + (7.5)P = 409.

 

Substituting C = 60 - P in the expression above,

 

(6.5) (60 - P) + (7.5)P = 409, that is, 390 - (6.5)P + (7.5)P = 409, that is, (1.5)P = 19, so that

 

P = 19/(1.5) = 12 + (2/3) pounds.

 

C = 60 - P = 47 + (1/3) pounds.

 

Ariel, for my sake, please do the back-check and confirm that the answer is correct.  If it is not, please post a comment.  Thanks.

 

Dattaparbhakar (Dr. G.)