Siblings savings distribution

Three siblings saved a combined total of CZK 1,445. Adela saved 10% less than Martin, and David saved 10% more than Adela. How many crowns did each of them save?

Final Answer:

D =  495 Kc
A =  450 Kc
M =  500 Kc

Step-by-step explanation:

$$\begin{gathered} a=100\%-10\%=1-\frac{10}{100}=0.9 \\ d=100\%+10\%=1+\frac{10}{100}=1.1 \\ A+M+D=1445 \\ A=a\cdot M \\ D=d\cdot A \\ A=0.9\cdot M \\ D=1.1\cdot A \\ A+D+M=1445 \\ A-0.9M=0 \\ 1.1A-D=0 \\ Pivot:Row1\leftrightarrow Row3 \\ Row2-\frac{1}{1.1}\cdot Row1\to Row2 \\ 0.909D-0.9M=0 \\ Row3-\frac{1}{1.1}\cdot Row1\to Row3 \\ 1.909D+M=1445 \\ Pivot:Row2\leftrightarrow Row3 \\ Row3-\frac{0.90909091}{1.90909091}\cdot Row2\to Row3 \\ -1.376M=-688.095 \\ M=\frac{-688.0952381}{-1.37619048}=500 \\ D=\frac{1445-M}{1.90909091}=\frac{1445-500}{1.90909091}=495 \\ A=\frac{0+D}{1.1}=\frac{0+495}{1.1}=450 \\ A=450 \\ D=495 \\ M=500 \end{gathered}$$

Try another example