Peter crown ratio

Peter has only two crowns in the treasury and can divide them both in a ratio of 4:5 and in a ratio of 4:7. How many crowns does Peter have in the money box if the amount saved is less than 300 CZK?

Final Answer:

x₁ =  198 Kc

Step-by-step explanation:

$$\begin{gathered} a=4+5=9 \\ b=4+7=11 \\ 9=3^2 \\ 11...\text{ prime number} \\ LCM(9,11)=3^2\cdot 11=99 \\ d=2\cdot LCM(a,b)=2\cdot LCM(9,11)=198 \\ x<300 \\ {x}_1=d=198=198\text{Kc} \\ \text{ Verifying Solution: } \\ {p}_1=\frac{4}{4+5}\cdot x_1=\frac{4}{4+5}\cdot 198=88 \\ {p}_2=\frac{5}{4+5}\cdot x_1=\frac{5}{4+5}\cdot 198=110 \\ {p}_3=\frac{4}{4+7}\cdot x_1=\frac{4}{4+7}\cdot 198=72 \\ {p}_4=\frac{7}{4+7}\cdot x_1=\frac{7}{4+7}\cdot 198=126 \end{gathered}$$

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