2 coffees are combined costing $5.50 per pound and $3.00 per pound? How many lbs of each should be used to make 50 lb of a blend costing $3.70 per lb?

Question

A coffee merchant combines coffee costing $5.50 per pound with coffee costing $3.00 per pound. How many pounds of each should be used to make 50 lb of a blend costing $3.70 per pound? 

Answer 1

Let x be the amount of coffee in the blend costing $5.50 per pound.  Since we are blending 50 lbs, the amount of $3.00 per pound coffee in the blend will be 50-x pounds.

 

($3.70)*(50 lbs) = ($5.50)*(x lbs) + ($3.00)*(50-x lbs)

 

$185 = 5.5x + 150 - 3x

 

$35 = 2.5x

 

Solve for x, the amount of $5.50 coffee in the blend.  Once you have x, the amount of $3 coffee in the blend is 50 lbs - x.