Question:
The circle graph below represents the opinions of $100$ students about their favorite sports. Each student chose exactly one of these four options: Basketball, Hockey, Football, and Other. The following statements are true about the graph:

$\bullet$  The number of students who chose Basketball is three times the number of students who chose Other.

$\bullet$  Ten more students chose Football than chose Hockey.

$\bullet$  The percent of students who chose Basketball plus the percent of students who chose Football equal $65\%.$

What percent of the students chose Basketball?

[asy]
draw(circle((0,0),1),linewidth(2));
draw((0,0)--(0,1),linewidth(2));
draw((0,0)--dir(-35),linewidth(2));
draw((0,0)--dir(137),linewidth(2));
draw((0,0)--dir(-115),linewidth(2));

label("Other",1.2*dir(100));
label("Football",1.5*dir(10));
label("Hockey",1.2*dir(-80));
label("Basketball",1.6*dir(180));

label("Favorite Sports of 100 Students",(0,1.5));
[/asy]

Answer:
Since there are $100$ students, the percent of students who chose each sport is the same as the number of students who chose it. Let $x$ be the number of students who chose Basketball. From the first statement, the number of students who chose Other is $\dfrac{x}{3}.$ From the third statement, the number of students who chose Football is $65-x.$ Combining this with the second statement, $55-x$ students chose Hockey. Since a total of $100$ students were interviewed, we have $x + \frac{x}{3} + (65-x) + (55-x) = 100.$ Solving, we get $x = 30,$ so $\boxed{30\%}$ chose Basketball.