Theater 60503

We will pay 445 euros for 50 tickets. How many cinema and theater tickets will we pay if one cinema ticket costs 4 euros and a theater ticket 11 euros?

Correct answer:

d =  35
k =  15

Step-by-step explanation:

$$\begin{gathered} k+d=50 \\ 4k+11d=445 \\ k+d=50 \\ 4\cdot k+11\cdot d=445 \\ d+k=50 \\ 11d+4k=445 \\ Pivot:Row1\leftrightarrow Row2 \\ 11d+4k=445 \\ d+k=50 \\ Row2-\frac{1}{11}\cdot Row1\to Row2 \\ 11d+4k=445 \\ 0.64k=9.55 \\ k=\frac{9.54545455}{0.63636364}=15 \\ d=\frac{445-4k}{11}=\frac{445-4\cdot 15}{11}=35 \\ d=35 \\ k=15 \end{gathered}$$

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