Saplings 31521

The orchard was planted over three years. In the second year, 15% more saplings were planted than in the first year. In the third year, 40% fewer saplings were planted than in the first and second years combined. A total of 4,128 saplings were planted. How many saplings were planted in each year?

Final Answer:

a =  1200
b =  1380
c =  1548

Step-by-step explanation:

$$\begin{gathered} r_1=100\%+15\%=1+\frac{15}{100}=1.15 \\ {r}_2=100\%-40\%=1-\frac{40}{100}=0.6 \\ b=r_1\cdot a \\ c=r_2\cdot (a+b) \\ a+b+c=4128 \\ b=1.15\cdot a \\ c=0.6\cdot (a+b) \\ a+b+c=4128 \\ 1.15a-b=0 \\ 0.6a+0.6b-c=0 \\ a+b+c=4128 \\ Row2-\frac{0.6}{1.15}\cdot Row1\to Row2 \\ 1.15a-b=0 \\ 1.122b-c=0 \\ a+b+c=4128 \\ Row3-\frac{1}{1.15}\cdot Row1\to Row3 \\ 1.15a-b=0 \\ 1.122b-c=0 \\ 1.87b+c=4128 \\ Pivot:Row2\leftrightarrow Row3 \\ 1.15a-b=0 \\ 1.87b+c=4128 \\ 1.122b-c=0 \\ Row3-\frac{1.12173913}{1.86956522}\cdot Row2\to Row3 \\ 1.15a-b=0 \\ 1.87b+c=4128 \\ -1.6c=-2476.8 \\ c=\frac{-2476.8}{-1.6}=1548 \\ b=\frac{4128-c}{1.86956522}=\frac{4128-1548}{1.86956522}=1380 \\ a=\frac{0+b}{1.15}=\frac{0+1380}{1.15}=1200 \\ a=1200 \\ b=1380 \\ c=1548 \end{gathered}$$

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