Respuesta :
Answer:
There were 49 people that chose chocolate and vanilla twist.
Step-by-step explanation:
This problem can be solved by building a Venn diagram of this set, where:
-A is the number of the people that tasted the vanilla
-B is the number of the people that tasted the chocolate.
The most important information in this problem is that some of those people tasted both. It means that [tex]A \cap B = x[/tex], and x is the value we want to find.
The problem states that 97 people tasted the vanilla sample of frozen yogurt. This includes the people that tasted both samples. It means that x people tasted the chocolate and vanilla twist and 97-x people tasted only the vanilla twist.
72 people tasted the chocolate, also including the people that tasted both samples. It means that x people that tasted the chocolate and vanilla twist and 72-x that tasted only the chocolate twist.
So, recapitulating, there are 120 people, and
97-x tasted only the vanilla twist.
72 - x tasted only the chocolate twist
x people tasted both
So
97 - x + 72 - x + x = 120
-x = 120 - 72 - 97
-x = -49 *(-1)
x = 49
There were 49 people that chose chocolate and vanilla twist.
