Money ratio division

Kuba, Martin, and Pete earned CZK 1,813. They divided them in the ratio Cuba: Martin 6:5. Martin: Pete 2:3. How many crowns did each of them get?

Final Answer:

K =  588 Kc
M =  490 Kc
P =  735 Kc

Step-by-step explanation:

$$\begin{gathered} a=1813\text{Kc} \\ K:M=6:5=12:10 \\ M:P=2:3=10:15 \\ K:M:P=12:10:15 \\ d=\frac{a}{12+10+15}=\frac{1813}{12+10+15}=49\text{Kc} \\ K=12\cdot d=12\cdot 49=588\text{Kc} \end{gathered}$$

$M=10\cdot d=10\cdot 49=490\text{Kc}$

$$\begin{gathered} P=15\cdot d=15\cdot 49=735=735\text{Kc} \\ \text{ Verifying Solution: } \\ {r}_1=K:M=588:490=\frac{6}{5}=1.2=6:5 \\ {r}_2=M:P=490:735=\frac{2}{3}\doteq 0.6667=2:3 \\ s=K+M+P=588+490+735=1813\text{Kc} \end{gathered}$$

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