Respuesta :
Answer:
For plan B to save money car rental need to drive 111.1 miles as [tex]\frac{x}{y}[/tex] expresses the average amounts of miles per day car rental drive and its obtained value is 111.1.
Step-by-step explanation:
In the question it is given that a car rental company offers two plans for renting a car.
Plan A: $30 per day and [tex]$\$ 0 \cdot 18$[/tex] per mile.
Plan B: $50 per day with free unlimited mileage
It is required to find that how many miles would be needed to drive for plan B to save money. be needed to drive for plan B to save money.
Step 1 of 5
In Plan A $30 per day and [tex]$\$ 0 \cdot 18$[/tex] per mile are costed so the cost of Plan A is given by following equation,
[tex]$A=30 y+0 \cdot 18 x$[/tex]
In Plan B $50 per day with free unlimited mileage are costed so the cost of Plan B is given by following equation,
[tex]$B=50 y$[/tex]
Step 2 of 5
Now comparing the obtained equations [tex]$A=30 y+0 \cdot 18 x$[/tex]
and B=50y.
[tex]$30 y+0 \cdot 18 x=50 y$[/tex]
Step 3 of 5
Subtract 30y from both the sides of the obtained equation 30 y+0.18x=50y and simplify using subtraction properties.
[tex]$30 y+0 \cdot 18 x-30 y=50 y-30 y$\\ $0 \cdot 18 x=20 y$[/tex]
Step 4 of 5
Divide both the sides of the obtained equation [tex]$0 \cdot 18 x=20 y$[/tex] by [tex]$0 \cdot 18$[/tex] and simplify using division properties.
[tex]$\begin{aligned}&\frac{0 \cdot 18 x}{0 \cdot 18}=\frac{20 y}{0.18} \\&x=\frac{1000 y}{9}\end{aligned}$[/tex]
Step 5 of 5 save money car rental need to drive 111.1 miles.
[tex]$\begin{aligned}&\frac{x}{y}=\frac{1000 y}{9 y} \\&\frac{x}{y}=111.1\end{aligned}$[/tex]
