Question

Ulysses is spending his vacation in South Carolina. He rents a car and is offered two different payment options. He can either pay $25.00 each day plus $0.15 per mile (option A) or pay $10.00 each day plus $0.40 per mile (option B). Ulysses rents the car for one day.
Write an inequality representing the number of miles where option A will be the cheaper plan. (set up the inequality and then step by step how to solve)
How many miles will Ulysses have to drive for option A to be the cheaper option?
Please show step by step work

Answer 1

Hi there! First things first, we would set the inequality up like this: 25 + 0.15m < 10 + 0.40m. We set this up, because we are looking for A to be the better option and it’s only being rented for a day. Subtract 0.40m from both sides to get 25 - 0.25m < 10. This is because the number with the variable on the left side is now s negative. Now, subtract 25 to get -0.25m < -15. Now, divide each side by -0.25 to isolate the variable. When you do, you get m > 60. This is because you divided by a negative number, so you flip the symbol over to the opposite. Driving 60 miles will get you the same price, but Ulysses will have to drive 61 miles for option A to be cheaper.

Answer 2

The inequality that is set up and solved is as follows:

0.15x +25 < 0.40x +10     x represents the number of miles and the inequality is set up to make option a cheaper.

 0.15x +25 < 0.40x +10
 -0.15x         -0.15x                 Subtract 0.15x from both sides to get the variable on one side

 25> 0.40x + 10
-10             -10                    Subtract 10 from both sides to isolate the variable

    15> 0.40x
÷0.40   ÷0.40                        Divide both sides by 0.40 to isolate the variable          
60 < x

This shows that if the miles are greater than 60 miles then option A is cheaper. If the miles are less than 60, then option B is cheaper