How many pounds of bread crumbs at $1.00 per pound must be added to two pounds of ground beef at $5.00 per pound to make a meatloaf that costs $3.50 per pound?

Question

How many pounds of bread crumbs at $1.00 per pound must be added to two pounds of ground beef at $5.00 per pound to make a meatloaf that costs $3.50 per pound?

Answer 1

Let B = pounds of bread crumbs

Let G = pounds of ground beef  

 

Total weight of meatloaf = B + G

Total cost of meatloaf = 1.00*B + 5.00*G 

Cost of meatloaf (per pound) = (1.00*B + 5.00*G) / (B+G) = 3.50

 

Two pounds of ground beef  ==>  G = 2

 

Plug this value for G into the cost per pound equation 

 

(B + 10) / (B + 2) = 3.5

B + 10 = 3.5*B + 7

2.5*B = 3

B = 3/2.5 = 30/25 = 6/5 pounds of bread crumbs 

 

Check:  Total weight = 6/5 + 2 = 16/5 pounds

            Total cost = 1*(6/5) + 5*2 = 6/5 + 10 = $56/5

             Cost per pound = (56/5) / (16/5) = (56/5)*(5/16) = 56/16 = 7/2 = $3.50