Prizes - competition

For the prizes for the three best competitors a sum of money in crowns was prepared.
The first competitor got half of this sum.
The second competitor got 300 crowns.
The third competitor got the rest of the prepared amount, which was three times less crowns than the first competitor got.

A. How many times more crowns did the second competitor get than the third competitor?

B. How many crowns were prepared in total for the prizes?

Final Answer:

x =  2
n =  900 Kc

Step-by-step explanation:

$$\begin{gathered} a=n/2 \\ b=300 \\ c=(n-n/2-b)=n/2-300 \\ c=a/3 \\ c=n/6 \\ n/6=n/2-300 \\ 2n=1800 \\ n=\frac{1800}{2}=900 \\ n=900 \\ a=n/2=900/2=450\text{Kc} \\ b=300\text{Kc} \\ c=a/3=450/3=150\text{Kc} \\ x=b/c=300/150=2 \end{gathered}$$

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