A group of 80 students in a college are surveyed. They are asked which of Spanish or French they are studying. a) complete the Venn Diagram. b) How many students study ONLY French c) How many students study Spanish?

a) Find attached the completed Venn diagram (2nd diagram)

b) 25

c) 46

A related Question found at (ID 16765143):

A group of 80 students in a college are surveyed. They are asked which of Spanish or French they are studying. 71 of the students surveyed studies at least one of the two languages.

a) Complete the Venn diagram.

b) How many students study only french?

c) How many students study Spanish?

Step-by-step explanation:

Find attached the Venn diagram (1st diagram)

a) Total number of students in college = 80

Since 71 out of the 80 students surveyed studies at least one of the two languages, the number of students that studied neither French nor Spanish = 80-71 = 9

From the venn diagram:

Number of students that study Spanish = 14

Number of students that study French = 25

We need to determine if the values are for Spanish only and French only respectively or for at least Spanish and French respectively.

Estimated value for the middle term = 80-(14+25+9) = 32

From the above calculation, the number of students that study both Spanish and French is 32 and it is more than each set value. This implies the value given in the Venn diagram is for Spanish only and French only respectively.

Let number of students that study both Spanish and French = x

Spanish only = 14

French only = 25

the number of students that studied neither French nor Spanish = 9

Total:

14 + 25 + x + 9 = 80

48 + x = 80

x = Number of students that study both Spanish and French = 32

b) French only = 25

c) Number of  students that study Spanish = students that study at least Spanish

= 14+x = 14+32

Number of  students that study Spanish = 46

a² + b²= c²

24² + 7² = c²

c= 25