On an indoor circular track of circumference 50 feet, Joneal starts at point $S$, runs in a counterclockwise direction, and then stops when he has run exactly one mile (5280 feet). On which quarter of the circle, $A$, $B$, $C$ or $D$, did Joneal stop?

[asy]
import graph;
draw(Circle((0,0),20));
draw((-25,0)--(25,0));
draw((0,-25)--(0,25));
dot((20,0));
label("$S$",(20,0),SE);
label("$A$",(17,17),E);
label("$B$",(-17,17),W);
label("$C$",(-17,-17),W);
label("$D$",(17,-17),E);
[/asy]
Since 5250 is divisible by 50, Joneal is back at point $S$ after running 5250 feet.  For the next 12.5 feet, he is on the portion of the track marked $A$. For the next 12.5 feet after that, he is on the portion of the track marked $B$.  At this point he has traveled $5250+12.5+12.5=5275$ feet.  After traveling the final 5 feet, he is on the portion of the track marked $\boxed{C}$.
C
Level 4
Prealgebra
Problem: On an indoor circular track of circumference 50 feet, Joneal starts at point $S$, runs in a counterclockwise direction, and then stops when he has run exactly one mile (5280 feet). On which quarter of the circle, $A$, $B$, $C$ or $D$, did Joneal stop?

[asy]
import graph;
draw(Circle((0,0),20));
draw((-25,0)--(25,0));
draw((0,-25)--(0,25));
dot((20,0));
label("$S$",(20,0),SE);
label("$A$",(17,17),E);
label("$B$",(-17,17),W);
label("$C$",(-17,-17),W);
label("$D$",(17,-17),E);
[/asy]
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine the quarter of the circle where Joneal stops, first calculate how many complete laps he runs on the track. The circumference of the track is 50 feet. To find the number of laps in one mile, divide the total distance Joneal runs by the circumference of the track:

5280 feet / 50 feet = 105.6 laps.

This means Joneal completes 105 full laps and then runs an additional 0.6 of a lap. To find the distance he runs after completing 105 laps, multiply the number of laps by the circumference:

105 laps * 50 feet/lap = 5250 feet.

Next, calculate the remaining distance he runs after completing 105 laps:

5280 feet - 5250 feet = 30 feet.

Now, determine where Joneal is after running an additional 30 feet from the starting point $S$. Since the track is circular and divided into four quarters, each quarter is:

50 feet / 4 = 12.5 feet.

Starting from point $S$, the distances to the quarter points are as follows:

- Quarter $A$: 0 to 12.5 feet
- Quarter $B$: 12.5 to 25 feet
- Quarter $C$: 25 to 37.5 feet
- Quarter $D$: 37.5 to 50 feet

Since Joneal runs 30 feet, he moves past quarter $A$ (12.5 feet) and quarter $B$ (25 feet), and then continues into quarter $C$. The distance of 30 feet places him within the range of quarter $C$, specifically between 25 feet and 37.5 feet. Therefore, Joneal stops in quarter $C$.<|END_OF_LATENT|> The final answer is $C$.