School pupil distribution

A total of 1415 pupils attend the three primary schools. They go to the second school twice as much as to the first, and to the third, they go 100 less than to the second. How many pupils attend the third school?

Final Answer:

c =  506

Step-by-step explanation:

$$\begin{gathered} a+b+c=1415 \\ b=2\cdot a \\ c=b-100 \\ a+b+c=1415 \\ 2a-b=0 \\ b-c=100 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 1.5b+c=1415 \\ Row3-\frac{1}{1.5}\cdot Row2\to Row3 \\ -1.667c=-843.333 \\ c=\frac{-843.33333333}{-1.66666667}=506 \\ b=\frac{1415-c}{1.5}=\frac{1415-506}{1.5}=606 \\ a=\frac{0+b}{2}=\frac{0+606}{2}=303 \\ a=303 \\ b=606 \\ c=506 \end{gathered}$$

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