Question

There are 25 students in Mrs. Pietz's fifth grade class at an international school. All of the students speak either English or Japanese, and some speak both languages of the students, 16 can speak English and 14 can speak Japanese. (a) How many speak both English and Japanese? (b) How many speak English, but not Japanese? (Hint: Draw a Venn diagram.) (a) How many speak both English and Japanese? ____students (b) How many speak English, but not Japaneso? ______students

Answer 1

Number of students who speak both English and Japanese = 5 students

Number of students who speak English but not Japanese = 11 students

Thus option a and b are correct.

Step-by-step explanation:

To solve this problem, let's use a Venn diagram to represent the number of students who speak English, Japanese, and both languages.

Given:

Total students = 25

Students who speak English = 16

Students who speak Japanese = 14

From this information, we know that the total number of students who speak at least one of the languages is 25, which is the union of students who speak English (16) and students who speak Japanese (14).

Using the formula for the union of sets:

Total students = Students who speak English + Students who speak Japanese - Students who speak both languages

25 = 16 + 14 - Students who speak both languages

Students who speak both languages = 16 + 14 - 25

Students who speak both languages = 30 - 25

Students who speak both languages = 5

Now, to find the number of students who speak English but not Japanese, we subtract the number of students who speak both languages from the total number of students who speak English:

Students who speak English but not Japanese = Students who speak English - Students who speak both languages

Students who speak English but not Japanese = 16 - 5

Students who speak English but not Japanese = 11

Therefore, the number of students who speak both English and Japanese is 5, while the number of students who speak English but not Japanese is 11.

Thus option a and b are correct.