How many non-negative integer solutions does the equation $3x + y + z = 24$ have? If the equation is $x + y + z = 24$ then it is solvable with stars and bars theorem.  But what to do if it is $3x + y + z = 24$? 

Put $x=0\;,$ Then $y+z=24$. So we get Total ordered pair of $(y,z)$ is $= 25$
Put $x=1\;,$ Then $y+z=21$. So we get Total ordered pair of $(y,z)$ is $= 22$
Put $x=2\;,$ Then $y+z=18$. So we get Total ordered pair of $(y,z)$ is $= 19$
Put $x=3\;,$ Then $y+z=15$. So we get Total ordered pair of $(y,z)$ is $= 16$
Put $x=4\;,$ Then $y+z=12$. So we get Total ordered pair of $(y,z)$ is $= 13$
Put $x=5\;,$ Then $y+z=9$. So we get Total ordered pair of $(y,z)$ is $= 10$
Put $x=6\;,$ Then $y+z=6$. So we get Total ordered pair of $(y,z)$ is $= 7$
Put $x=7\;,$ Then $y+z=3$. So we get Total ordered pair of $(y,z)$ is $= 4$
Put $x=8\;,$ Then $y+z=0$. So we get Total ordered pair of $(y,z)$ is $= 1$
So total no. of ordered triples $(x,y,z)$ is $ = 25+22+19+16+13+10+7+4+1=$
