Question

A grocery wants to mix 2 kinds of coffee. One kind sells for a dollar per pound, and the other sells for $2.55 per pound. He wants to mix a total of 28 pounds and sell it for $1.35 per pound. How many pounds of each kind should he use in the new mix?

a) 12 pounds of the $1 coffee and 16 pounds of the $2.55 coffee
b) 14 pounds of the $1 coffee and 14 pounds of the $2.55 coffee
c) 16 pounds of the $1 coffee and 12 pounds of the $2.55 coffee
d) 18 pounds of the $1 coffee and 10 pounds of the $2.55 coffee

Answer 1

The grocery should use 12 pounds of the $1 coffee and 16 pounds of the $2.55 coffee.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's assume the number of pounds of the $1 coffee is x, and the number of pounds of the $2.55 coffee is y. We know that the total weight is 28 pounds, so we have the equation:

x + y = 28

We also know that the total cost per pound of the mixture is $1.35, so we can set up another equation:

(1 * x + 2.55 * y) / 28 = 1.35

Simplifying the second equation, we get:

x + 2.55 * y = 37.8

Now we can solve the system of equations. Using substitution or elimination method, we find that the solution is x = 12 and y = 16. Therefore, the grocery should use 12 pounds of the $1 coffee and 16 pounds of the $2.55 coffee.