Question

A yogurt stand gave out 120 free samples of frozen yogurt, one free sample per person. The three sample choices were vanilla, chocolate, or chocolate & vanilla twist. 97 people tasted the vanilla and 72 people tasted the chocolate, some of those people tasted both because they chose the chocolate and vanilla twist. How many people chose chocolate and vanilla twist?

Answer 1

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 $A \cap B = x$, 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.