the coffee merchant plans to mix some francy $6.50 per pound ground coffe called royal soi with 10 pounds of a lowly $2 per ground coffee called pleasant peasant to create a $4 per pound ground coffe called royal peasant. How many pounds of the $6.50 per pound ground coffee should he use?

Answer 1

Let x be the number of pounds of the $6.50 per pound ground coffee called Royal Soi.

We know that the total weight of the new blend is the sum of the weights of the two individual coffees. So:

x + 10 = total weight

We also know that the cost of the new blend is the weighted average of the costs of the two individual coffees. So:

(6.5x + 2(10)) / (x + 10) = 4

Now, we can solve for x:

(6.5x + 20) / (x + 10) = 4
6.5x + 20 = 4x + 40
2.5x = 20
x = 8

The coffee merchant should use 8 pounds of the $6.50 per pound ground coffee called Royal Soi.