Question

parking in a student lot costs $1 for the first half hour, and 1.75 for each hour there after. A partial hour is charged the same as a full hour. What is the longest time that a student can park in the lot for $8.00

Answer 1

Make a list of how many hours you park, and how much it will cost.

Answer 2

grind it til you find it
up to one half hour $1
up to one and a half hours $2.75
up to two and a half hours $4.50 etc

Answer 3

Rule: Charged by full hours, no partial hours. Limit of $8.

Convert Rates to a common unit, Hours: 1.) First 30 minutes (x): $1*2 = $2/hr
2.) Remaining time (y): $1.75/hr
We will find that t= x+y
x= 30min./60min. = .5
y=unknown
$8 = The most we can pay.
So we know this: 1.) $8 = $2*(x) + $1.75*(y), where x=.5hrs and y=remaining time
2.) $8 = $2*(.5) + $1.75*(y)
3.) $8 = $1 + $1.75*(y), now we subtract $1 from both sides
-$1 -$1
4.) $8-$1 = $1.75*(y), we get this equation afterward
5.) $7 = $175(y), now we divide by $1.75 on both sides
/$1.75 /$1.75
6.) $7/$1.75 = (y), we get this equation afterward
7.) $7/$1.75 = 4, so y=4

So now we know x=.5 and y=4.

Our total time equation is t=x+y. So, let's plug in our values for x and y.
1.) t = x+y
2.) t = .5 + 4
3.) 4.5 = .5 + 4

But we have to pay the full hour because there are no partial hours. So, 4.5 would cost the same as 5 hours. Since we don't have anymore money, we can't pay for 5 hours of parking. We need to round down to the nearest full hour. In this case, rounding down will give us 4 hours.

So our answer is 4 hours of parking. And, we will have $1.75*(.5)=$87.5 cents left in our wallet.

I hope that helps.

Answer 4

make a proportion