Question

Laura's Coffee Shop makes a blend that is mixture of two types of coffee. Type A coffee costs Laura $5.65 per pound, and type B coffee costs $4.35 per pound. This month, Laura made 158 pounds of the blend, for a total cost of $775.70. How many pounds of type A coffee did she use?

Answer 1

`a=68\: lbs,\: b=90\: lbs`

1) We can solve this problem by setting up a System of Linear Equations. So, based on this text, we can write out the following equations:

`\begin{gathered} 5.65a+4.35b=775.70 \\ a+b=158 \end{gathered}`

Note that the first equation relates itself to the total cost, and the second one to the amount of blend.

2) Now, we can solve this system of Linear Equations by the Elimination Method. Let's multiply the second equation by -5.65 so that we can add them both and eliminate "a"

`\begin{gathered} 5.65a+4.35b=775.70 \\ -5.65a-5.65b=-892.7 \\ ---------------- \\ -1.3b=-117 \\ (-1.3b)/(-1.3)=(-117)/(-1.3) \\ b=90 \end{gathered}`

Now, we can plug into the second equation b=90 and then solve it for a:

`\begin{gathered} a+b=158 \\ a+90=158 \\ a+90-90=158-90 \\ a=68 \end{gathered}`

Thus, the answer is:

`a=68\: lbs,\: b=90\: lbs`