Programmers 3247

The three programmers received a reward of 21,000 euros for their joint work. They received the money according to the work done. The first got 20% less than the second, and the third got 50% more than the first. How much did each of them receive?

Correct answer:

a =  5600 eur
b =  7000 eur
c =  8400 eur

Step-by-step explanation:

$$\begin{gathered} k=100\%-20\%=1-\frac{20}{100}=0.8 \\ q=100\%+50\%=1+\frac{50}{100}=1.5 \\ a+b+c=21000 \\ a=k\cdot b \\ c=q\cdot a \\ a+a/k+q\cdot a=21000 \\ a+a/0.8+1.5\cdot a=21000 \\ 3.75a=21000 \\ a=\frac{21000}{3.75}=5600 \\ a=5600=5600\text{eur} \end{gathered}$$

$b=a/k=5600/0.8=7000\text{eur}$

$c=q\cdot a=1.5\cdot 5600=8400\text{eur}$

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