inequalities

Question

a car can be rented  from Johny's Car Rental for $2000 per day with no charge for mileage or from Car Rental Exclusive for $1000 per day plus $20 for each kilometer driven. If a car is to be rented from Car Rental Exclusive, for how many kilometers of intended travel does it cost less to rent from Johny's Car Rental?

Answer 1

Johnny’s Car Rental = $2000 Per Day

Car Rental Exclusive = $1000 + $20k (k is for kilometers)

The inequality set up would be: $2000 < $1000 + $20k

You then want to solve for k.

$2000 < $1000 + $20k

-$1000 < -$1000

$1000 < $20k

$1000/$20 < $20k/$20

50 < k or another way to write it is k > 50.

So where the number of kilometers is Greater than 50, Johnny’s Car Rental would be cheaper.

Answer 2

With any word problem, your first step is to determine what the question is asking.  In this case, you are asked to find the number of kilometers multiplied by $20 that will be more than the difference between $2000 and $1000.  So let's do the math:

$2000 - $1000 = $1000:  This is the amount that your multiplication must be more than to correctly answer the question.  So now we can set up the equation.  We'll denote kilometers with the letter k.

20 x k > 1000

k > 1000/20

k > 50

Because the question asks for the number of kilometers that will make renting from Johny's car rental less expnsive, you must add 1 to the right side of your equation, making the correct answer 51 kilometers.