Question

74. REAL-WORLD APPLICATIONS

A car rental company offers two plans for renting a car. Plan A: $30 per day and $0.18 per mile Plan B: $50 per day with free unlimited mileage How many miles would you need to drive for plan B to save you money?

Answer 1

For plan B to save money car rental need to drive 111.1 miles as
`(x)/(y)` expresses the average amounts of miles per day car rental drive and its obtained value is 111.1.

Explanation:

In the question it is given that a car rental company offers two plans for renting a car.

Plan A: $30 per day and
`$\$ 0 \cdot 18$` 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 $30 per day and
`$\$ 0 \cdot 18$` per mile are costed so the cost of Plan A is given by following equation,

`$$A=30 y+0 \cdot 18 x$$`

In Plan B $50 per day with free unlimited mileage are costed so the cost of Plan B is given by following equation,

`$$B=50 y$$`

Step 2 of 5

Now comparing the obtained equations
`$A=30 y+0 \cdot 18 x$`

and B=50y.

`$$30 y+0 \cdot 18 x=50 y$$`

Step 3 of 5

Subtract 30y from both the sides of the obtained equation 30 y+0.18x=50y and simplify using subtraction properties.

`$$30 y+0 \cdot 18 x-30 y=50 y-30 y$$\\ $0 \cdot 18 x=20 y$`

Step 4 of 5

Divide both the sides of the obtained equation
`$0 \cdot 18 x=20 y$` by
`$0 \cdot 18$` and simplify using division properties.

`$$\begin{aligned}&(0 \cdot 18 x)/(0 \cdot 18)=(20 y)/(0.18) \\&x=(1000 y)/(9)\end{aligned}$$`

Step 5 of 5 save money car rental need to drive 111.1 miles.

`$$\begin{aligned}&(x)/(y)=(1000 y)/(9 y) \\&(x)/(y)=111.1\end{aligned}$$`