A coffee

A coffee shop owner blends a gourmet brand of coffee with a cheaper brand. Gourmet coffee usually sells for R420,00 per kilogram, while the cheaper brand sells for R180,00 per kilogram. How much of each type should be mixed to have 30 kilograms of coffee worth R240,00 per kilogram?

Correct answer:

a =  7.5 kg
b =  22.5 kg

Step-by-step explanation:

$$\begin{gathered} m=30\text{kg} \\ a+b=m \\ 420.00\cdot a+180.00\cdot b=240.00\cdot m \\ a+b=30 \\ 420.00\cdot a+180.00\cdot b=240.00\cdot 30 \\ a+b=30 \\ 420a+180b=7200 \\ Pivot:Row1\leftrightarrow Row2 \\ 420a+180b=7200 \\ a+b=30 \\ Row2-\frac{1}{420}\cdot Row1\to Row2 \\ 420a+180b=7200 \\ 0.57b=12.86 \\ b=\frac{12.85714286}{0.57142857}=22.5 \\ a=\frac{7200-180b}{420}=\frac{7200-180\cdot 22.5}{420}=7.5=7.5\text{kg} \\ a=\frac{15}{2}=7.5 \\ b=\frac{45}{2}=22.5 \end{gathered}$$

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