Question

A coffee merchant combines coffee that costs $5 per pound with coffee that costs $3.50 per pound. How many pounds of each should be used to make 25 lb of a blend costing $4.43 per pound?

Answer 1

Let x be pounds of $5 coffee and y be pounds of $3.50 coffee which equals the total pounds of coffee:

x + y = 25

The total cost of blended coffee is calculated by adding the total cost of the two different coffees together:

5.00(x) + 3.50(y) = 4.43(25)

To solve for one variables use the substitution method:

x + y = 25

x = 25 - y

5(25-y) + 3.5y = 110.75

125 - 5y + 3.5y = 110.75

-1.5y = -14.25

y = 9.5lb

x = 25-9.5

= 15.5lb

So it takes 15.5lb of the $5/lb coffee and 9.5lb of the $3.50/lb coffee to make 25lb of the blended coffee at $4.43lb.

Hope This Helps!