Question

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, and type B coffee costs $4.25 per pound. This month, Rafael made 139 pounds of the blend, for a total cost of $706.75. How many pounds of type B coffee did he use? a) 45 pounds b) 50 pounds c) 55 pounds d) 60 pounds

Answer 1

Rafael used 50 pounds of type B coffee.

Step-by-step 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
`\(A + B = 139\)`.

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:

`\[5.70A + 4.25B = 706.75\]`

Now, we have a system of two equations:

`\[ \begin{cases} A + B = 139 \\ 5.70A + 4.25B = 706.75 \end{cases} \]`

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:

`\[5.70 * 89 + 4.25 * 50 = 706.75\]`

Hence, the final answer is that Rafael used 50 pounds of type B coffee.