1). A coffee merchant combines coffee that costs $5 per pound with coffee that costs $3.20 per pound.

Question

How many pounds of each should be used to make 26 lb of a blend costing $4.55 per pound?

Answer 1

Let's say there are a pounds of $5 coffee and b pounds of $3.20 coffee.  Since there are two unknowns, we need two equations and they would be:

 

5a + 3.20b = 4.55(26)

a + b = 26

 

Solve for a and substitute

 

a = 26 - b

5(26 - b) + 3.2b = 4.55(26)

130 - 5b + 3.2b = 118.3

-1.8b = -11.7

b = 6.5

 

So we should use 6.5 pounds of the $3.20 per pound coffee.  Now substitute 6.5 for b in one of the first two equations to find a, the amount of $5 per pound coffee to use.