Question

The sugar sweet company will choose from two companies to transport its sugar to market. The first company charges $2808 to rent trucks plus an additional fee of $50.25 for each ton of sugar. The second company does not charge to rent trucks but charges $225.75 for each ton of sugar.

Answer 1

First let's write the equations of cost for each company, for the first company we have:

`c=2808+50.25s`

Where "c" is the cost and "s" is the tons of sugar.

For the second company, we have

`c=225.75s`

Therefore if we want to know when the tons and the cost will be equal, we must solve the system of equations:

`\begin{cases}c=2808+50.25s{} \\ c=225{.75s}\end{cases}`

Look that we have two equations for c, then we say that

`225.75s=2808+50.25s`

And solve it for "s"

`\begin{gathered} 225.75s=2808+50.25s \\ \\ 225.75s-50.25s=2808 \\ \\ 175.5s=2808 \\ \\ s=(2808)/(175.5)=16 \end{gathered}`

Therefore for 16 tons of sugar the cost will be the same, now we put 16 on one of the equations to find it

`\begin{gathered} c=225.75s \\ \\ c=225.75*16 \\ \\ c=3612 \end{gathered}`

Therefore for 16 tons of sugar, the cost will be $3612 for both companies.