The number of boxes at 3 hours from the opening can be written as:
[tex]\begin{gathered} 52\cdot3+b=404 \\ 156+b=404 \\ b=404-156 \\ b=248 \end{gathered}[/tex]The term 52 * 3 represents the number of boxes produced in the 3 hours, so b is the initial stock.
As the sum of the boxes produced and the initial stock is 404, b is equal to 248.
To complete the table we use the relation:
[tex]y=248+52x[/tex]Replacing the values for x, we can find the value of y:
[tex]\begin{gathered} x=0\to y=248+52\cdot0=248 \\ x=1\to y=248+52\cdot1=248+52=300 \\ x=2\to y=248+52\cdot2=248+104=352 \\ x=3\to y=248+52\cdot3=248+156=404 \end{gathered}[/tex]Answer: the initial stock is 248 boxes.