There are two types of ice cream cones, chocolate and vanilla. You and 24 of your friends (25 total people) are going to buy ice cream cones. If 15 people buy vanilla cones, and 20 people buy chocolate cones, how many people bought both chocolate and vanilla ice cream cones?
25 people bought 35 cones
so 10 people bought both
5 only van - 10 both - 10 only choc
Help me po
To find the number of people who bought both chocolate and vanilla ice cream cones, we need to find the intersection between the two groups (people who bought vanilla and people who bought chocolate cones).
Given:
Total number of people = 25
Number of people who bought vanilla cones = 15
Number of people who bought chocolate cones = 20
To find the number of people who bought both types of cones, we can use the principle of inclusion-exclusion. First, we add the number of people who bought vanilla and chocolate cones together:
15 + 20 = 35
Since 35 is greater than the total number of people (25), we have double-counted some individuals who bought both types of cones.
To find the number of people who bought both types of cones, we subtract the number of double-counted individuals:
35 - 25 = 10
Therefore, 10 people bought both chocolate and vanilla ice cream cones.
To find the number of people who bought both chocolate and vanilla ice cream cones, we can use the concept of sets and set operations.
Let's assume that the set of people who bought vanilla cones is represented by V and the set of people who bought chocolate cones is represented by C. Given that 15 people bought vanilla cones (|V| = 15) and 20 people bought chocolate cones (|C| = 20), we need to find the size of the intersection of these two sets, denoted by V ∩ C.
We can use the principle of inclusion-exclusion to find the size of the intersection. The principle states that:
|V ∪ C| = |V| + |C| - |V ∩ C|
Here, |V ∪ C| represents the size of the union of V and C (which is the total number of people who bought either vanilla or chocolate cones).
Given that there are a total of 25 people (you and 24 friends), we can substitute the values into the equation as follows:
25 = 15 + 20 - |V ∩ C|
Simplifying the equation:
25 = 35 - |V ∩ C|
Subtracting 35 from both sides:
-10 = -|V ∩ C|
To solve for |V ∩ C|, we need to eliminate the negative sign by multiplying both sides by -1:
10 = |V ∩ C|
Therefore, 10 people bought both chocolate and vanilla ice cream cones.