Sets And Relations Question 1
Question 1 - 2024 (01 Feb Shift 1)
The number of elements in the set
$S={(x, y, z): x, y, z \in \mathbf{Z}, x+2 y+3 z=42, x, y, z$
$\geq 0}$ equals
Show Answer
Answer (169)
Solution
$$ \begin{array}{ll} x+2 y+3 z=42, & x, y, z \geq 0 \ z=0 & x+2 y=42 \Rightarrow 22 \ z=1 & x+2 y=39 \Rightarrow 20 \ z=2 & x+2 y=36 \Rightarrow 19 \ z=3 & x+2 y=33 \Rightarrow 17 \ z=4 & x+2 y=30 \Rightarrow 16 \ z=5 & x+2 y=27 \Rightarrow 14 \ z=6 & x+2 y=24 \Rightarrow 13 \ z=7 & x+2 y=21 \Rightarrow 11 \ z=8 & x+2 y=18 \Rightarrow 10 \ z=9 & x+2 y=15 \Rightarrow 8 \ z=10 & x+2 y=12 \Rightarrow 7 \ z=11 & x+2 y=9 \Rightarrow 5 \ z=12 & x+2 y=6 \Rightarrow 4 \ z=13 & x+2 y=3 \Rightarrow 2 \ z=14 & x+2 y=0 \Rightarrow 1 \end{array} $$
Total : 169
