Fair

Several students from our class went on excursions. Everyone paid the same amount. In the end, there were a few euros left that needed to be returned to them. If we returned 3 euros to each person, there would still be 5 euros left. If we returned 4 euros to each person, there would be 20 euros missing. How many cents should we give each of them to return this money fairly?

Correct answer:

x =  20

Step-by-step explanation:

$$\begin{gathered} n\cdot 3=z-5 \\ n\cdot 4=z+20 \\ 4n-3n=(z+20)-(z-5) \\ n=20-(-5)=25 \\ z=n\cdot 3+5=25\cdot 3+5=80\text{eur} \\ a=z/n=80/25=\frac{16}{5}=3\frac{1}{5}=3.2\text{eur} \\ x=100\cdot (a-3.0)=100\cdot (3.2-3.0)=20 \end{gathered}$$

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