Ladislav in Amsterdam

Larry was sent to a conference in Amsterdam as a reward. The conference fee was €1702.

Calculate how many books Larry could buy at prices of 30 and 28 euros each, given that he does not want to fill his entire home library and may buy only 59 books in total.

Final Answer:

x =  25
y =  34

Step-by-step explanation:

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

Try another example