Henry Ernest Dudeney/Puzzles and Curious Problems/158 - Newsboys/Working

== Working for by : $158$ -- Newsboys ==

The simultaneous equations in matrix form:


 * $\begin {pmatrix}

-1 & 0 &  0 &  0 &  0 &  4 \\ -1 &  0 &  0 &  0 &  4 &  1 \\ -1 &  0 &  0 &  4 &  1 &  1 \\ -1 &  0 &  4 &  1 &  1 &  1 \\ -1 &  1 &  1 &  1 &  1 &  1 \\ 0 &  0 & -1 &  1 & -1 &  1 \\ \end {pmatrix} \begin {pmatrix} n \\ J_J \\ J_C \\ S_N \\ J_B \\ S_T \end {pmatrix} = \begin {pmatrix} 4 \\ 4 \\ 4 \\ 4 \\ 0 \\ 100 \end {pmatrix}$

when converted to reduced echelon form, gives:
 * $\begin {pmatrix}

1 & 0 &  0 &  0 &  0 &  0 \\ 0 &  1 &  0 &  0 &  0 &  0 \\ 0 &  0 &  1 &  0 &  0 &  0 \\ 0 &  0 &  0 &  1 &  0 &  0 \\ 0 &  0 &  0 &  0 &  1 &  0 \\ 0 &  0 &  0 &  0 &  0 &  1 \\ \end {pmatrix} \begin {pmatrix} n \\ J_J \\ J_C \\ S_N \\ J_B \\ S_T \end {pmatrix} = \begin {pmatrix} 1020 \\ 320 \\ 108 \\ 144 \\ 192 \\ 256 \end {pmatrix}$