Tickets 10

There are two types of zoo tickets: A for adults and C for children and senior citizens. The cost of 7 type A and 4 type C tickets is 46 €, whereas the cost of 8 type A and 6 type C tickets is 57 €. Calculate the cost of 5 type A and 3 type C tickets.

Correct answer:

x =  33.3 eur

Step-by-step explanation:

$$\begin{gathered} 7\cdot A+4\cdot C=46 \\ 8\cdot A+6\cdot C=57 \\ 7A+4C=46 \\ 8A+6C=57 \\ Pivot:Row1\leftrightarrow Row2 \\ 8A+6C=57 \\ 7A+4C=46 \\ Row2-\frac{7}{8}\cdot Row1\to Row2 \\ 8A+6C=57 \\ -1.25C=-3.88 \\ C=\frac{-3.875}{-1.25}=3.1 \\ A=\frac{57-6C}{8}=\frac{57-6\cdot 3.1}{8}=4.8 \\ A=\frac{24}{5}=4.8 \\ C=\frac{31}{10}=3.1 \\ x=5\cdot A+3\cdot C=5\cdot 4.8+3\cdot 3.1=33.3\text{eur} \end{gathered}$$

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