Respuesta :
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:
[tex]x+y=190...(1)[/tex]
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:
[tex]4.75x+2.5y=(3.80)190...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]4.75x+2.5(190-x)=(3.80)190[/tex]
[tex]4.75x+475-2.5x=722[/tex]
[tex]2.25x=722-475[/tex]
[tex]2.25x=247[/tex]
[tex]x=\frac{247}{2.25}[/tex]
[tex]x=109.777\approx 109.8[/tex]
Therefore, Sarah should use 109.8 pounds of high quality beans.
Upon substituting [tex]x=109.8[/tex] in equation (1), we will get:
[tex]109.8+y=190\\y=190-109.8\\y=80.2[/tex]
Therefore, Sarah should use 80.2 pounds of cheaper beans.
