Question

A grocer wants to mix two kinds of coffee. One kind sells for $1.15 per pound, and the other sells for $2.85 per pound. He wants to mix a total of 16 pounds and sell it for $2.10 per pound. How many pounds of each kind should he use in the new mix? (Round off the answers to the nearest hundredth.)

Answer 1

Let x the number of pounds of the first kinf od coffe, and y the number of punds of the second kind of coffe. Due to teh grocer wants to mix a total of 16 pounds you can write the following equation:

x + y = 18 (1)

Now, consider that the grocer also wants to sell the mixture of the two kind of coffes for $2.10 per pound. It means that the total earning for the sale of the mixed coffe is:

$2.10*16 = $33.6

Then, based on the previous amount and based on the price per pound for each kind of coffe is $1.15 and $2.85 respectively, you can write:

1.15x + 2.85y = 33.6 (2)

Then, you have a system of two equations with two incognits. To solve it, proceed as follow:

Multiply equation (1) by -1.15 and sum the result to equation (2) to cancel out x and solve for y:

(x + y = 16)(-1.15)

-1.15x - 1.15y = -18.4

-1.15x - 1.15y = -18.4

1.15x + 2.85y = 33.6

1.7y = 15.2

y = 15.2/1.7

y = 8.94

Now, replace the previous value into the equation (1) and solve for x:

x + 8.94 = 16

x = 16 - 8.94

x = 7.06

Hence, the grocer should use 7.06 pounds of the first kind of coffe and 8.94 pounds of the second kind.s