A group of friends consists of 12 people who like either football or basketball.

A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like both, how many like only basketball?

A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like both, how many like only basketball?

Step 1: Identify the total number of friends, which is 12.
Step 2: Identify how many like football, which is 7.
Step 3: Identify how many like both football and basketball, which is 5.
Step 4: Use the formula: Total = Football + Basketball - Both.
Step 5: Substitute the known values into the formula: 12 = 7 + B - 5.
Step 6: Simplify the equation: 12 = 7 + B - 5 becomes 12 = 2 + B.
Step 7: Solve for B (the number of basketball players): B = 12 - 2, so B = 10.
Step 8: To find how many like only basketball, subtract those who like both from the total basketball players: Only Basketball = B - Both = 10 - 5.
Step 9: Calculate: Only Basketball = 5.

Set Theory – Understanding the relationships between different groups and how to calculate the number of elements in overlapping sets.
Venn Diagrams – Using visual representations to solve problems involving overlapping groups.
Basic Algebra – Applying algebraic manipulation to solve for unknowns in equations.