Ladislav in Amsterdam

Laco went (was sent) to a conference in Amsterdam for a reward. The conference fee was € 1702.

Calculate how many books Ladislav could buy at the price of 30 and 28 euros if he doesn't want to fill the whole home library, and he can buy only 59 books.

Correct answer:

x =  25
y =  34

Step-by-step explanation:

$$\begin{gathered} x+y=59 \\ 30\cdot x+28\cdot y=1702 \\ x+y=59 \\ 30x+28y=1702 \\ Pivot:Row1\leftrightarrow Row2 \\ 30x+28y=1702 \\ x+y=59 \\ Row2-\frac{1}{30}\cdot Row1\to Row2 \\ 30x+28y=1702 \\ 0.07y=2.27 \\ y=\frac{2.26666667}{0.06666667}=34 \\ x=\frac{1702-28y}{30}=\frac{1702-28\cdot 34}{30}=25 \\ x=25 \\ y=34 \end{gathered}$$

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