Hamburger seller price

Two sellers, each in their stand, sold hamburgers at the same price, expressed as a natural number in CZK greater than 30. The first seller received 1260 CZK, and the second received only 792 CZK. How much CZK did 1 hamburger cost? How many hamburgers did the first sell, and how many did the second seller sell?

Final Answer:

p =  36 Kc
a =  35
b =  22

Step-by-step explanation:

$$\begin{gathered} p>30 \\ 1260=a\cdot p \\ 792=b\cdot p \\ 1260=2^2\cdot 3^2\cdot 5\cdot 7 \\ 792=2^3\cdot 3^2\cdot 11 \\ \text{GCD}(1260,792)=2^2\cdot 3^2=36 \\ d=GCD(1260,792)=36 \\ p=d=36\text{Kc}=36\text{Kc} \end{gathered}$$

$a=1260/d=1260/36=35$

$b=792/d=792/36=22$

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