3. After conducting a survey among 96 sixth-grade students at his school, Leo drew a bar chart as shown in the image, but he did not highlight the numbers on the vertical axis or the names of the sports on the horizontal axis. He remembered that there are five times more students who swim than those who play tennis, and twice as many as those who play handball. There are fewer basketball players than water polo players. How many students play basketball?

![](https://cdn.mathpix.com/cropped/2024_06_03_47603db0a075197c1d6ag-5.jpg?height=599&width=902&top_left_y=1628&top_left_x=583)
Another solution.

From the condition of the problem that "five times more students swim than play tennis" and the ratio of the height of the third and the first column, we conclude that the third column represents swimmers, and the first column represents tennis players.

Let the number of students who play tennis be $x$ (1st column).

Then, $5x$ students swim (3rd column), and $2.5x$ students play handball (4th column). $\quad 1$ POINT

From the diagram, it can be observed, since there are fewer basketball players than water polo players, that $1.5x$ students play basketball (2nd column), and $2x$ students play water polo (5th column). 1 POINT

The equation holds: $\quad x+1.5x+5x+2.5x+2x=96 . \quad 1$ POINT

It follows that $\quad 12x=96$

$x=8$

1 POINT

The number of basketball players is $1.5 \cdot 8$, i.e., 12 students play basketball.

$1$ POINT

TOTAL 6 POINTS