Number of integer solutions of $3x+y+z=23$

Question

Calculate the number of nonnegative integer solutions of $$3x+y+z=23.$$

Answer 1

Hint:

Start from $x=0$ and you get $y+z=23$ and the total ordered pair $(y,z)=24$

Continue taking $x=0,1,2,....$ until it is non-negative and then add all the ordered pairs of $(y,z)$ to get the number of non-negative integer solutions.