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16.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?

Respuesta :

Answer:7

Step-by-step explanation:

This can be solved by Venn-diagram

Given there  are total 5 students who want french and Latin

also 3 among them want Spanish,french & Latin

i.e. only 2 students wants both french and Latin only.

Also Student who want only Latin is 5

Thus Student who wants Latin and Spanish both only is 11-5-3-2=1

Students who want only Spanish is 8 Thus students who wants Spanish and French is 4

Similarly Students who wants Only French is 16-4-3-2=7

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Lanuel

Based on the calculations, the number of students that want French only is 7 students.

What is a Venn diagram?

A Venn diagram can be defined as a circular graphical (visual) tool that is used to represent, logically compare and contrast two (2) or more finite sets of data such as objects, students, events, concepts, etc.

Note: The similarities between two sets of data in a Venn diagram is indicated by an intersection of the two (2) circles.

From the Latin circle:

Both French and Latin (FnL) = 5 students.

All three subjects = 3 students.

French and Latin only = [tex]5 -3[/tex] = 2 students.

Only Latin = 5 students.

Latin and Spanish only = [tex]11-(5+3+2)[/tex] = 1 student.

From the Spanish circle:

Both French and Spanish (FnS) = 4 students.

From the French circle:

[tex]F+2+3+4+1+8+5=30\\\\F+23=30\\\\F=30-23[/tex]

French only, F = 7 students.

Read more on Venn diagram here: https://brainly.com/question/24581814

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