6. At Chili's school, there are 92 freshmen. Every freshman can choose between Latin, Spanish, Italian or no

language. They may also take more than one language class if they choose to. 42 freshmen take Spanish, 36 take

Latin and 51 take Italian. 15 take all three classes, 12 take just Latin and Spanish, 3 take only Latin and 4 take

only Spanish.

How many students take only Latin?

How many students do not take any of the three language classes?

Use the Venn diagram to solve this question. Start from the common area for three languages. It is known that three languages take 15 freshmen. Then go to the common area for two languages - Spanish and Latin take 12. If 3 persons take only Latin and 36 take Latin, then 36-3-12-15=6 - the number of people that selected Latin and Italian.

4 freshmen take only Spanish, 12 take Spanish and Latin, 15 take all three languages and 42 take Spanish, then 42-12-15-4=11 - the number of people that selected Spanish and Italian.

11 freshmen take Spanish and Italian, 6 take Italian and Latin, 15 take all three languages and 51 take Italian, then 51-11-6-15=19 - the number of people that selected only Italian.

Together 4+12+3+11+15+6+19=70 freshmen. If at school are 92 freshmen, then any of the three language classes take 92-70=22 freshmen.

Answer: only Latin take 3 persons and any of the three language classes take 22 person.