We appreciate your visit to Rafael s Coffee Shop makes a blend that is a mixture of two types of coffee Type A coffee costs Rafael 5 70 per pound. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final Answer:
Rafael used 50 pounds of type B coffee.
Explanation:
Let's denote the pounds of type A coffee as A and the pounds of type B coffee as B. The problem states that Rafael made 139 pounds of the blend, so [tex]\(A + B = 139\)[/tex].
The cost of type A coffee is $5.70 per pound, and the cost of type B coffee is $4.25 per pound. The total cost is $706.75, and we can express this in terms of the weights and costs:
[tex]\[5.70A + 4.25B = 706.75\][/tex]
Now, we have a system of two equations:
[tex]\[ \begin{cases} A + B = 139 \\ 5.70A + 4.25B = 706.75 \end{cases} \][/tex]
Solving this system, we find that A = 89 and B = 50. Therefore, Rafael used 50 pounds of type B coffee.
This can be confirmed by substituting these values back into the total cost equation:
[tex]\[5.70 \times 89 + 4.25 \times 50 = 706.75\][/tex]
Hence, the final answer is that Rafael used 50 pounds of type B coffee.
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