To solve this problem using a Venn diagram, we need to start by drawing a rectangle to represent the group of 50 students, and then draw two overlapping circles to represent the subjects of Math and Science. Let's label the regions of the Venn diagram as follows:
- M: Students who like Math
- S: Students who like Science
- MS: Students who like both Math and Science
- Neither: Students who like neither Math nor Science
We know that 20 students like only Math, 15 students like only Science, and the number of students who like both subjects is unknown. We also know that the number of students who like neither subject is double the number of students who like both subjects. Let's use this information to fill in the Venn diagram:
- The number of students who like at least one subject is the sum of the students who like only Math, the students who like only Science, and the students who like both subjects: 20 + 15 + MS.
- The number of students who like neither subject is double the number of students who like both subjects: 2MS.
We can set up an equation using this information:
20 + 15 + MS + 2MS = 50
Simplifying this equation, we get:
3MS = 15
MS = 5
Now we can fill in the Venn diagram:
M MS
\ /
\/
/ \
S----MS
We know that MS = 5, so the number of students who like at most one subject is:
20 (like only Math) + 15 (like only Science) + MS (like both subjects) = 20 + 15 + 5 = 40.
Therefore, 40 students in the group of 50 like at most one subject.