First let's write the equations of cost for each company, for the first company we have:
[tex]c=2808+50.25s[/tex]
Where "c" is the cost and "s" is the tons of sugar.
For the second company, we have
[tex]c=225.75s[/tex]
Therefore if we want to know when the tons and the cost will be equal, we must solve the system of equations:
[tex]\begin{cases}c=2808+50.25s{} \\ c=225{.75s}\end{cases}[/tex]
Look that we have two equations for c, then we say that
[tex]225.75s=2808+50.25s[/tex]
And solve it for "s"
[tex]\begin{gathered} 225.75s=2808+50.25s \\ \\ 225.75s-50.25s=2808 \\ \\ 175.5s=2808 \\ \\ s=\frac{2808}{175.5}=16 \end{gathered}[/tex]
Therefore for 16 tons of sugar the cost will be the same, now we put 16 on one of the equations to find it
[tex]\begin{gathered} c=225.75s \\ \\ c=225.75\times16 \\ \\ c=3612 \end{gathered}[/tex]
Therefore for 16 tons of sugar, the cost will be $3612 for both companies.
