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Three classmates, Alena, Barbora, and Cecílie, were supposed to divide a certain amount of money. Alena got A Eur, Barbora got B Eur and Cecílie got C Eur. In the division, A: B=9:7 and B: C=6:13 applied. Alena and Cecílie received €1,450 together. How many euros did Barbora get?

Correct answer:

B =  420 EUR

Step-by-step explanation:

$$\begin{gathered} A:B=9:7 \\ B:C=6:13\doteq 0.4615=6:13 \\ A+C=1450 \\ 7\cdot A=9\cdot B \\ 13\cdot B=6\cdot C \\ A+C=1450 \\ 7A-9B=0 \\ 13B-6C=0 \\ A+C=1450 \\ Row3-\frac{1}{7}\cdot Row1\to Row3 \\ 7A-9B=0 \\ 13B-6C=0 \\ 1.286B+C=1450 \\ Row3-\frac{1.28571429}{13}\cdot Row2\to Row3 \\ 7A-9B=0 \\ 13B-6C=0 \\ 1.593C=1450 \\ C=\frac{1450}{1.59340659}=910 \\ B=\frac{0+6C}{13}=\frac{0+6\cdot 910}{13}=420=420\text{EUR} \\ A=\frac{0+9B}{7}=\frac{0+9\cdot 420}{7}=540 \\ A=540 \\ B=420 \\ C=910 \end{gathered}$$

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