Venn Diagram

4. A guidance counselor is planning schedules for 30 students. Sixteen students say they want to take French, 16 want to take Spanish, and 11 want to take Latin. Five say they want to take both French and Latin, and of these, 3 wanted to take Spanish as well. Five want only Latin, and 8 want only Spanish. How many students want French only?

• Start with the Latin circle. You have sufficient information to determine how many students want both Latin and Spanish (1).
  

• Using this new information, you can work within the Spanish circle to determine how many students want both Spanish and French (4).
  

• Using this new information, you can work within the French circle to determine how many students want French only (7).
  

• The last step could be represented algebraically as

x + 4 + 3 + 2 + 5 + 8 + 1 = 30
x + 23 = 30
x = 7