Question

Manuel's coffee shop makes a blend that is a mixture of two types of coffee. type A coffee costs Manuel $4.35 per pound, and type B coffee cost $5.45 per pound. this month, Manuel made 175 pounds of the blend, for a total cost of $866.85 how many pounds of type A coffee did he use

Answer 1

Step 1

Type A coffee costs $4.35 per pound

Type B coffee cost $5.45 per pound.

Manuel made 175 pounds of the blend at a total cost of $866.85

Required; To find how many pounds of type A coffee used.

Step 2

Write a system of equation

`\begin{gathered} 4.35A+5.45B=866.85--(1) \\ A+B=175---(2) \end{gathered}`

Step 3

Find the value of A

`\begin{gathered} \text{From 2} \\ B=175-A \\ \text{Substituting this in 1 gives} \\ 4.35A+5.45(175-A)=866.85 \\ 4.35A+953.75-5.45A=866.85 \\ 953.75-866.85=5.45A-4.35A \\ 86.9=1.1A \\ (1.1A)/(1.1)=(86.9)/(1.1) \\ A=79\text{ pounds} \end{gathered}`

Hence, Manuel used 79 pounds of type A coffee