Contract payment distribution

The client paid the three partners CZK 90,000 for the completed contract. 40% of this amount was the material and 23% that the remaining amounts were paid for insurance and taxes. They divided the rest of the money in the ratio of 2:3:5. What amount did each get?

Final Answer:

a =  8316 Kc
b =  12474 Kc
c =  20790 Kc

Step-by-step explanation:

$$\begin{gathered} x=90000\text{Kc} \\ r=40\%=\frac{40}{100}=\frac{2}{5}=0.4 \\ d=23\%=\frac{23}{100}=0.23 \\ y=x-r\cdot x=90000-0.4\cdot 90000=54000\text{Kc} \\ z=y-d\cdot y=54000-0.23\cdot 54000=41580\text{Kc} \\ a:b:c=2:3:5 \\ k=\frac{z}{2+3+5}=\frac{41580}{2+3+5}=4158\text{Kc} \\ a=2\cdot k=2\cdot 4158=8316\text{Kc} \end{gathered}$$

$b=3\cdot k=3\cdot 4158=12474\text{Kc}$

$c=5\cdot k=5\cdot 4158=20790\text{Kc}$

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