ANSWER:
Company A is cheaper than Company B when t > 6 hours
STEP-BY-STEP EXPLANATION:
The first thing we must do is raise the equation for each company.
[tex]\begin{gathered} \text{Company A} \\ A=50t+300 \\ \text{Company B} \\ B=75t+150 \end{gathered}[/tex]
where t is number of hours.
Graph each equation and we have:
We give various values to t, to generate the points to graph, just like this
[tex]\begin{gathered} \text{Company A} \\ A=50\cdot0+300=300\rightarrow(0,300) \\ A=50\cdot5+300=550\rightarrow(5,550) \\ A=50\cdot10+300=800\rightarrow(10,800) \\ \text{ Company B} \\ B=75\cdot0+150=150\rightarrow(0,150) \\ B=75\cdot5+150=525\rightarrow(5,525) \\ B=75\cdot10+150=900\rightarrow(10,900) \end{gathered}[/tex]
Company A is the black line and company B is the red line
Solving for when Company A is cheaper than Company B
[tex]\begin{gathered} 50t+300<75t+150 \\ 50t-75t<150-300 \\ -25t<-150 \\ 25t>150 \\ t>\frac{150}{25} \\ t>6 \end{gathered}[/tex]
