Final answer:
There are 38 boys who belong to only the football team at the high school, after considering the overlaps with the wrestling and baseball teams, and adjusting for those who are on all three teams.
Step-by-step explanation:
To solve this question, we can use the principle of inclusion-exclusion in sets to find out how many boys belong to only the football team. We start off with the total number of boys on the football team, which is 42. Then, we need to subtract the number of boys who are on both the football and wrestling teams, and both the football and baseball teams, and finally add back the members who are part of all three teams, because they have been subtracted twice. According to the question, there are 12 boys on both the baseball and football teams, and 8 of those are on all three teams. So the number of boys only on the football team would be:
- Total football team members: 42
- Members on both football and baseball: 12
- Members on all three teams: 8 (already subtracted once in the 12)
Now we perform the calculation: Only football team members = 42 (total) - 12 (both football and baseball) + 8 (all three teams, to adjust for double subtraction) = 38. Finally, we must consider boys who are on both the football and wrestling teams but aren't included in the previous groups. As the problem doesn't provide this specific intersection, we assume it to be only the boys that are in all three sports since any other members on the football and wrestling team but not baseball would already be counted as purely football members.
So, the number of boys belonging only to the football team is 38.