## Emilyggarza 3 years ago parking in a student lot cost $1 for the first hour and 1.75 for each hour there after a partial hour is changed the same as a full hour what is the longest time that a student can park in this lot for$7 ? the longest time is ? have to show my work.

1. etemplin

the expression for how much money it costs is 1+1.75t where t is time in hours. If the cost has to be less than or equal to 7, set the expression less than or equal to 7 1+1.75t<=7 subtract 1 from both sides and divide by 1.75 this will tell you how many hours you can have remember to round down to the nearest integer

2. hitten101

1+1.75t<=7 1.75t<=6 calculate t now..

3. Emilyggarza

okay

4. Emilyggarza

the answer is 6

5. etemplin

@hitten101 i think we both made a mistake...shouldnt it be 1+1.75(t-1)<=7 because if you plug in 1 hour into the original, you get charged 2.75 not 1.00

6. Emilyggarza

okay

7. hitten101

oh yes you are right @etemplin

8. Emilyggarza

the answer is 6 then?

9. Emilyggarza

no offends you a very intelligent handsome guy.

10. etemplin

no. using the new equation (the old one was wrong...sorry about that) you get t<=4.42 so it should be 4. ill check by taking 1 for the first hour, adding 1.75 for the second hour (total = 2.75) add 1.75 for the third hour (total = 4.5) and 1.75 for the 4th hour (total = 6.25) since you cant go over 7, the hours = 4

11. hitten101

No @etemplin the time can go in fractions also. it does not need to be a natural number. it can be a fraction.

12. etemplin

it says if you only use a partial hour it counts for a whole one

13. hitten101

@Emilyggarza whom u referring to?

14. etemplin

not me ;)

15. hitten101

hmmm... ur right @etemplin i ignored that part of the question

16. hitten101

and thank you @Emilyggarza

17. robtobey

$1+\text{Floor}\left[\frac{7-1}{1.75}\right]=4 \text{ hours}$Floor[x] gives the greatest integer less than or equal to x.