Break even Point?

Question

The Break-Even Point?
Rent-A-Dent (RAD) has rental specials on compact cars:

a) Hondas rent for $25 per day and $.24 (24 cents) per mile.

b) Toyotas rent for $31 per day and $.19 (19 cents) per mile.

What is the break-even point for both rental cars, include the mileage and cost????

Answer 1

25*D + 0.24*M = 31*D + 0.19*M

0.05*M = 6*D

M/D= 120

So you see, the number of days rented AND the mileage are important here! There are in a infinite number of break-even points, depending upon the number of days you plan to have the car, and/or how many miles you plan to drive.

If you plan to have the car a fixed and stated number of days, then you can make a discrete calculation.

For example, if you rent the cars for one day (D=1), then the breakeven mileage = 120.
So: $25 + $0.24*120 = $53.80

Done.

Answer 2

31+.19X = 25+.24X
31-25=.19-.24X
6=.05X
X=6/.05 = 120
120 miles is the break even point
The costs is $25+(.24x120)= 25+28.80=$53.80 for the Honda and
$31+(.19x120) = 31+22.80=$53.80 for the Toyota
As pointed out above, you would have to travel the 120 miles each day of the rental

Answer 3

The break even point is 120 miles and $53.80 for each rental car.

Hondas: 25 + .24x
Toyota: 31 + .19x

At the Break Even point, both will be equal, so

25 + .24x = 31 + .19x
Subtract .19x from both sides and subtract 25 from both sides to get
.05x = 6
Divide both sides by .05
x = 120 miles

If you plan on driving less than 120, then rent a Honda
If you plan on driving more than 120 miles, then rent a Toyota

Of course this is good if you rent for only one day. Multiply 120 miles by number of days you rent to get the amended break-even miles and multiply $53.80 by the number of days you rent to get the amended break-even cost.

Answer 4

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Answer 5

The break even point depends on days and mileage
T= 25d+0.24m
H =31d+0.19m
25d+0.24m= 31d +0.19m
6d+0.05m=0
So the break even points are on a straight line
6x+0.05y =0 where x are the days and y the mileage
y=120x