# Break even Point?

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????

Relevance

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.

• 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

• 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.

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• 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