Wreaths 81547

Eva paid €8.4 for three wreaths and five creams. Jana paid €15.6 for 9 wreaths and 7 creams. How many crowns will Jan pay for one wreath and one cream?

Correct answer:

x =  2 Eur

Step-by-step explanation:

$$\begin{gathered} 3a+5b=8.40 \\ 9a+7b=15.6 \\ 3\cdot a+5\cdot b=8.40 \\ 9\cdot a+7\cdot b=15.6 \\ 3a+5b=8.4 \\ 9a+7b=15.6 \\ Pivot:Row1\leftrightarrow Row2 \\ 9a+7b=15.6 \\ 3a+5b=8.4 \\ Row2-\frac{3}{9}\cdot Row1\to Row2 \\ 9a+7b=15.6 \\ 2.67b=3.2 \\ b=\frac{3.2}{2.66666667}=1.2 \\ a=\frac{15.6-7b}{9}=\frac{15.6-7\cdot 1.2}{9}=0.8 \\ a=\frac{4}{5}=0.8 \\ b=\frac{6}{5}=1.2 \\ x=a+b=0.8+1.2=2\text{Eur} \end{gathered}$$

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