Improvement 23971

Three employees received a reward of CZK 5,000 for the improvement proposal. They divided the money according to work so that the first got twice as much as the second, and the second got three times as much as the third. How many crowns did each person receive?

Correct answer:

a =  3000 Kc
b =  1500 Kc
c =  500 Kc

Step-by-step explanation:

$$\begin{gathered} a+b+c=5000 \\ a=2b \\ b=3c \\ 2b+b+c=5000 \\ 3b+c=5000 \\ 3\cdot 3c+c=5000 \\ 3\cdot 3\cdot c+c=5000 \\ 10c=5000 \\ c=\frac{5000}{10}=500 \\ c=500 \\ b=3\cdot c=3\cdot 500=1500\text{Kc} \\ a=2\cdot b=2\cdot 1500=3000\text{Kc} \end{gathered}$$

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