A total of 100 students play on the Sports Academy’s soccer, track, or basketball teams. No student plays on more than one team. 61 of the students are boys. There are 36 students on soccer teams, 19 are on the girls’ soccer team. There are 35 students on basketball teams, 18 are on the boys’ basketball team. How many boys are on the track team?

Answer 1

Let's summarize the information provided:

• Total students = 100
• Total boys = 61
• Total students on soccer teams = 36
• Girls on soccer teams = 19
• Total students on basketball teams = 35
• Boys on basketball teams = 18

From the above data, we can determine the number of boys and girls on each team.

1. Soccer Team:

   • Total players on soccer teams = 36
   • Girls on soccer teams = 19
   • Therefore, boys on soccer teams = Total soccer players - Girls on soccer players \[ \text{Boys on soccer teams} = 36 - 19 = 17 \]

2. Basketball Team:

   • Total players on basketball teams = 35
   • Boys on basketball teams = 18 (given)
   • Therefore, girls on basketball teams = Total basketball players - Boys on basketball players \[ \text{Girls on basketball teams} = 35 - 18 = 17 \]

3. Summarizing Players:

   • Total boys counted so far: \[ \text{Boys on soccer} + \text{Boys on basketball} = 17 + 18 = 35 \]

4. Calculating Track Team Players:

   • Total boys = 61
   • Therefore, boys on the track team: \[ \text{Boys on track} = \text{Total boys} - \text{Boys on soccer} - \text{Boys on basketball} \] \[ \text{Boys on track} = 61 - 17 - 18 = 26 \]

Thus, the number of boys on the track team is \( \boxed{26} \).