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*2)+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>(10)/(0.75) \\ \\ h>(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=(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((40)/(3))+35 \\ P=60+35 \\ P=95 \end{gathered}`

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