Question

Parabola Skate Rental rents skate boards for $4.50 per hour with a rental fee of $3 Arc of Hawk Skate Rental rents skate boards for $5.25 per hour with a rental fee o $25. Part A: Define the variables and write two equations to represent each rental company. Variables: Parabola. Arc of Hawk

Answer 1

$P=4.50h+35$

Where P represents the total cost on Parabola skate and h the numbr of hours

$A=5.25h+25$

Where A represents the total cost on Arc o Hawka nd h the number of hours

h=2 for the second equation

$\begin{gathered} A=(5.25\times2)+25 \\ A=10.50+25 \\ A=35.50 \end{gathered}$

To know when the first store is cheaper than the second we compare the two equations using less than, so

$Pso[tex]4.50h+35<5.25h+25$

and solve for h

$\begin{gathered} 35-25<5.25h-4.50h \\ 10<0.75h \\ h>\frac{10}{0.75} \\ \\ h>\frac{40}{3}\approx13.3 \end{gathered}$

the first store will be cheaper when the skateboard is used for more than 13.3 hours

to know when they would cost the same we equal the equations

$\begin{gathered} P=A \\ 4.50h+35=5.25h+25 \end{gathered}$$h=\frac{40}{3}=13.3$

and if you need the coordinates, you can replace 40/3 on any equation to know the cost

so we can replace 40/3 on any equation, i will use the first

$\begin{gathered} P=4.50h+35 \\ P=4.50(\frac{40}{3})+35 \\ P=60+35 \\ P=95 \end{gathered}$

the cost is $95 and the coordinates ( 40/3 , 95 )