Step 1
Let x represent the number of workers in the company.
The total number of boxes assembled per day is 3600
The number of boxes compiled per person is y
Step 2
Write out the required equations.
[tex]\begin{gathered} xy=3600---(1) \\ x=\frac{3600}{y} \end{gathered}[/tex][tex]\begin{gathered} (x-3)(y+60)=3600---(2) \\ (\frac{3600}{y}-3)(y+60)=3600 \end{gathered}[/tex]Step 3
solve for y
[tex]\begin{gathered} -3y+\frac{216000}{y}+3420=3600 \\ -3y^2+216000+3420y=3600y \\ y=-300 \\ or \\ y=240 \end{gathered}[/tex]Hence each worker assembles 240 boxes daily since y cannot be negative.
Step 4
Find x
[tex]\begin{gathered} x=\frac{3600}{y} \\ x=\frac{3600}{240} \\ x=\text{ }15\text{ workers} \end{gathered}[/tex]Therefore, there are 15 workers on the manufacturing crew.
