The nutty professor sells cashews for $7.30 per pound and Brazil nuts for $4.50 per pound how much of each type should be used to make a 35 pound mixture that sells for $5.30 per pound.

Question

The nutty professor sells cashews for $7.30 per pound and Brazil nuts for $4.50 per pound how much of each type should be used to make a 35 pound mixture that sells for $5.30 per pound.

Answer 1

35lb mixture at $5.30/lb means that the total cost of that mixture is 35lbs * 5.30 $/lb = $185.5

Let C = the weight of cashews in the mixture.

Let B = the weight of Brazil nuts in the mixture.

7.3C + 4.5B = 185.5

C + B = 35

Have a system of equations.

C = 35 - B

7.3(35 - B) + 4.5B = 185.5

255.5 - 7.3B + 4.5B = 185.5

-2.8B + 255.5 = 185.5

-2.8B = 185.5 -255.5

-2.8B = -70

B = 70/2.8 = 25

C = 35 - B = 35 - 25 = 10

Mixture would then contain 25lbs of Brazil nuts and 10lbs of cashews.