Grade savings

Pupils of four grades saved n=45000 crowns together. Of this, the first year saved one-third, the second one-third of the remainder, the third two-fifths of the remainder, and the fourth the remainder.
How many crowns did each year save?

Final Answer:

a =  15000
b =  10000
c =  8000
d =  12000

Step-by-step explanation:

$$\begin{gathered} n=45000 \\ a=n/3=45000/3=15000 \end{gathered}$$

$b=\frac{1}{3}\cdot (n-a)=\frac{1}{3}\cdot (45000-15000)=10000$

$c=\frac{2}{5}\cdot (n-a-b)=\frac{2}{5}\cdot (45000-15000-10000)=8000$

$d=n-a-b-c=45000-15000-10000-8000=12000$

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