Final answer:
By setting up an equation where B represents the number of students in the basketball team and B + 10 represents the number of students in the volleyball team, we found that there are 27 basketball students and 37 volleyball students.
Step-by-step explanation:
In order to find out how many students are on each team, we need to set up an equation based on the information given. We are told that the total number of students in both teams is 64 and that the volleyball team has 10 more students than the basketball team.
Let's define B as the number of students in the basketball team. Therefore, the volleyball team would have B + 10 students since it has 10 more. The total adds up to 64, so we can write the following equation:
B + (B + 10) = 64
Solving for B, we combine like terms:
2B + 10 = 64
Then we subtract 10 from both sides:
2B = 54
Dividing both sides by 2 yields:
B = 27
Since B, the number of basketball players, is 27, we find the number of volleyball players by adding 10:
27 + 10 = 37
Thus, there are 27 basketball students and 37 volleyball students.