Question

Sarah Meeham blends coffee for​ Tasti-Delight. She needs to prepare 190 pounds of blended coffee beans selling for ​$3.80 per pound. She plans to do this by blending together a​ high-quality bean costing ​$4.75 per pound and a cheaper bean at ​$2.5?

Answer 1

Answer:

80.2 pounds of cheaper beans and 109.8 pounds of high quality beans.

Step-by-step explanation:

Let x represent pounds of high quality beans and y represent pounds of cheaper bean.

We have been given that Sarah needs to prepare 190 pounds of blended coffee beans. We can represent this information in an equation as:

$x+y=190...(1)$

We are also told that Sarah needs to prepare 190 pounds of blended coffee beans selling for ​$3.80 per pound. She plans to do this by blending together a​ high-quality bean costing ​$4.75 per pound and a cheaper bean at ​$2.5.

We can represent this information in an equation as:

$4.75x+2.5y=(3.80)190...(2)$

Upon substituting equation (1) in equation (2), we will get:

$4.75x+2.5(190-x)=(3.80)190$

$4.75x+475-2.5x=722$

$2.25x=722-475$

$2.25x=247$

$x=\frac{247}{2.25}$

$x=109.777\approx 109.8$

Therefore, Sarah should use 109.8 pounds of high quality beans.

Upon substituting $x=109.8$ in equation (1), we will get:

$109.8+y=190\\y=190-109.8\\y=80.2$

Therefore, Sarah should use 80.2 pounds of cheaper beans.