Question

A coffee merchant wants to make a mixture of 50 lb of Colombian and Brazilian coffees that will sell for

$3.19/lb. If Colombian coffee sells for $3.35/lb and Brazilian coffee sells for $2.95/lb, how much of each
type of coffee should be mixed together?

Answer 1

The merchant should mix 30 pounds of Colombian coffee and 20 pounds of Brazilian coffee.

Step-by-step explanation:

To find out how much of each type of coffee should be mixed together, we can use the method of weighted averages.

Let's assume that the merchant mixes x pounds of Colombian coffee and (50 - x) pounds of Brazilian coffee.

The cost per pound of the mixture is given by the equation:
(3.35x + 2.95(50 - x))/50 = 3.19

Simplifying the equation, we get:
3.35x + 2.95(50 - x) = 159.50

Expanding and combining like terms, we have:
3.35x + 147.5 - 2.95x = 159.50

Collecting terms, we get:
0.40x + 147.5 = 159.50

Subtracting 147.5 from both sides, we have:
0.40x = 12.00

Dividing both sides by 0.40, we get:
x = 30

Therefore, the merchant should mix 30 pounds of Colombian coffee and (50 - 30) = 20 pounds of Brazilian coffee.