Discounts on rail (ZSSK)

The railway company ZSSK offers a discount of 15% (REGIONAL) for 5 Eur/year. Calculate the real discount rate as a percentage, where passengers will travel 19 Eur per week.

Correct answer:

p =  14.6 %

Step-by-step explanation:

$$\begin{gathered} r=5+52\cdot 19=993 \\ q={\displaystyle \frac{100}{100-15}}={\displaystyle \frac{20}{17}}\doteq 1.1765 \\ b=52\cdot 19\cdot q=52\cdot 19\cdot 1.1765={\displaystyle \frac{19760}{17}}\doteq 1162.3529 \\ p=100\cdot {\displaystyle \frac{b-r}{b}}=100\cdot {\displaystyle \frac{1162.3529-993}{1162.3529}}=14.6\mathrm{\%} \end{gathered}$$

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