Parking/Car Problem: finding inequalities and bounded region

[KingAce]

Hi. I read an article about a parking/car service and was asked to answer a few math-related questions about it.

The expression for the amount that the trip will cost the parking/car service according to the lowest rate schedule- "$8 an hour and 40 cents a mile.

The maximum daily charge on the lowest rate schedule is $60, provided no more than 125 miles are traveled."- is C=8t + .40m (t represnts hours, while m is miles). I'm sure this expression is correct.

I also found 3 combinations of miles and hours that have a total cost of $60... 2 hrs = 110 miles, 4 hrs= 70 miles, and 5hrs= 50 miles. As Distance increases, Times decreases.

Question 3 asks, "The maximum daily rate is $60, provided that no more than 125 miles are traveled. WRITE 2 INEQUALITIES using m and t that express these constraints. .. then graph the region bounded by these inequalities (time along x-axis, miles along y).. it finally asks "Why isn't the point (t, m) = (1, 128) within the bounded region?

How do I find these inequalities? Can you point me in some direction or help me out? Thanks so much.

 

[stapel]

This last bit seems to follow from what came before. It would probably help if we had the full text of the exercise.

Thank you.

Eliz.

 

[Mrspi]

Re: Parking/Car Problem: finding inequalities and bounded re

Hi. I read an article about a parking/car service and was asked to answer a few math-related questions about it.

The expression for the amount that the trip will cost the parking/car service according to the lowest rate schedule- "$8 an hour and 40 cents a mile.

The maximum daily charge on the lowest rate schedule is $60, provided no more than 125 miles are traveled."- is C=8t + .40m (t represnts hours, while m is miles). I'm sure this expression is correct.

I also found 3 combinations of miles and hours that have a total cost of $60... 2 hrs = 110 miles, 4 hrs= 70 miles, and 5hrs= 50 miles. As Distance increases, Times decreases.

Question 3 asks, "The maximum daily rate is $60, provided that no more than 125 miles are traveled. WRITE 2 INEQUALITIES using m and t that express these constraints. .. then graph the region bounded by these inequalities (time along x-axis, miles along y).. it finally asks "Why isn't the point (t, m) = (1, 128) within the bounded region?

How do I find these inequalities? Can you point me in some direction or help me out? Thanks so much.

You've correctly written the "cost" equation:

C = 8t + .40m

Now, if the maximum daily rate is $60, that means the cost is less than or equal to 60. You should be able to write an inequality involving m and t to express this relationship.

It is also stated that the number of miles driven cannot exceed 125. So, the number of miles must be less than or equal to 125. You can write a second inequality involving m from this statement.