Tea blend

Tea blends are made from two kinds of tea. In standard tea, the mixture is two teas in a ratio of 1:3, and 40 g costs 42 CZK. In the premium tea mixture, weighing two teas in the 1:1 and 50 grams ratio costs 60 CZK. How much cost 10 grams of a more expensive kind of tea cost?

Final Answer:

x =  15 Kč

Step-by-step explanation:

$$\begin{gathered} m_1=40\text{g} \\ {m}_2=50\text{g} \\ {m}_3=10\text{g} \\ {r}_1=m_1/m_3=40/10=4 \\ {r}_2=m_2/m_3=50/10=5 \\ {r}_1\cdot (1x+3y)/(1+3)=42 \\ {r}_2\cdot (x+y)/(1+1)=60 \\ 4\cdot (1x+3y)/(1+3)=42 \\ 5\cdot (x+y)/(1+1)=60 \\ 4\cdot (1\cdot x+3\cdot y)/(1+3)=42 \\ x+3y=42 \\ 2.5x+2.5y=60 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{2.5}\cdot Row1\to Row2 \\ 2y=18 \\ y=\frac{18}{2}=9 \\ x=\frac{60-2.5y}{2.5}=\frac{60-2.5\cdot 9}{2.5}=15=15\text{Kc} \\ x=15 \\ y=9 \end{gathered}$$

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