Question

Jamila runs a grocery store that sells coffee beans blend by the pound.she wishes to mix 40 pounds of coffee to sell for a total cost of $222. to obtain the mixture she will mix coffee that sells for $5.10 per pound with coffee that sells for $6.30 per pound. how many pounds of each coffee should she use.

Answer 1

Let the $5.10 coffee be represented by x, and the $6.30 coffee be represented by y.

If she wishes to mix 40 pounds, this can be expressed as

$x+y=40\text{ ----------(1)}$

The total cost of both coffee is $222; this can be expressed as

$5.1x+6.3y=222\text{ -----------(2)}$

This provides a system of equations that can be solved simultaneously:

From equation 1, we can rewrite the equation to be

$x=40-y\text{ ----------(3)}$

Substitute equation 3 into equation 2:

$5.1(40-y)+6.3y=222$

Solving, we have

$\begin{gathered} 204-5.1y+6.3y=222 \\ -5.1y+6.3y=222-204 \\ 1.2y=18 \\ y=15 \end{gathered}$

To solve for x, substitute y = 15 into equation 3:

$\begin{gathered} x=40-15 \\ x=25 \end{gathered}$

Therefore, Jamila needs 25 pounds of the $5.10 coffee and 15 pounds of the $6.30 coffee.