Coffee 6

Coffee worth $1.05 per pound is mixed with coffee worth 85 cents per pound to obtain 20 pounds of a mixture worth 90 cents per pound. How many pounds of each type is used?

Correct answer:

a =  5 lb
b =  15 lb

Step-by-step explanation:

$$\begin{gathered} m=20\text{lb} \\ a+b=m \\ 1.05\cdot a+0.85\cdot b=0.90\cdot m \\ a+b=20 \\ 1.05\cdot a+0.85\cdot b=0.90\cdot 20 \\ a+b=20 \\ 1.05a+0.85b=18 \\ Pivot:Row1\leftrightarrow Row2 \\ 1.05a+0.85b=18 \\ a+b=20 \\ Row2-\frac{1}{1.05}\cdot Row1\to Row2 \\ 1.05a+0.85b=18 \\ 0.19b=2.86 \\ b=\frac{2.85714286}{0.19047619}=15 \\ a=\frac{18-0.85b}{1.05}=\frac{18-0.85\cdot 15}{1.05}=5=5\text{lb} \\ a=5 \\ b=15 \end{gathered}$$

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