Restaurant payment comparison

Four students were paying the bill in the restaurant. Jan paid 7 rums and 20 beers, Adam 20 rums and 7 beers, Víťa 12 rums and 25 beers, and Dan 25 rums and 12 beers. Jan paid 20% less than Adam. By how much % less did Víťa pay than Dan?

Final Answer:

p =  15 %

Step-by-step explanation:

$$\begin{gathered} j=7r+20p \\ a=20r+7p \\ v=12r+25p \\ d=25r+12p \\ {p}_1=100\%-20\%=1-\frac{20}{100}=0.8 \\ j=p_1\cdot a \\ 7r+20p=0.8\cdot (20r+7p) \\ r=1.6p \\ p=100\cdot \frac{d-v}{d} \\ p=100\cdot \frac{25r+12p-(12r+25p)}{25r+12p} \\ p=100\cdot \frac{25r+12p-(12r+25p)}{25r+12p} \\ p=100\cdot \frac{13r-13p}{25r+12p} \\ p=100\cdot \frac{13\cdot 1.6p-13p}{25\cdot 1.6p+12p} \\ p=100\cdot \frac{13\cdot 1.6-13}{25\cdot 1.6+12}=15\% \end{gathered}$$

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