S={(x, y, z): x, y, z in Z, x+2 y+3 z=42 math | vedclass

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Question

$x+2 y+3 z=42$,         $x, y, z \geq 0$

$z=0$        $x+2 y=42 \Rightarrow 22$

$z=1$

Vedclass · Accepted Answer

$169$

Vedclass · Answer

$x+2 y+3 z=42$,         $x, y, z \geq 0$

$z=0$        $x+2 y=42 \Rightarrow 22$

$z=1$        $x+2 y=39 \Rightarrow 20$

$z=2$         $x+2 y=36 \Rightarrow 19$

$z=3$         $x+2 y=33 \Rightarrow 17$

$z=4$          $x+2 y=30 \Rightarrow 16$

$z=5$          $x+2 y=27 \Rightarrow 14$

$z=6$          $x+2 y=24 \Rightarrow 13$

$z=7$          $x+2 y=21 \Rightarrow 11$

$z=8$          $x+2 y=18 \Rightarrow 10$

$z=9$          $x+2 y=15 \Rightarrow 8$

$z=10$        $x+2 y=12 \Rightarrow 7$ 

$z=11$         $x+2 y=9 \Rightarrow 5$

$z=12$         $x+2 y=6 \Rightarrow 4$

$z=13$         $x+2 y=3 \Rightarrow 2$

$z=14$         $x+2 y=0 \Rightarrow 1$

Total : $169$

$S=\{(x, y, z): x, y, z \in Z, x+2 y+3 z=42$ $\mathrm{x}, \mathrm{y}, \mathrm{z} \geq 0\}$ ...........

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