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Refer to the data below and answer the questions that follow.Super 100 Language Academy offers courses in four foreign languages: French, German, Spanish, and Chinese, serving a total of 400 students. Each student is enrolled in at least one language course and may be enrolled in multiple courses. The following are specifics regarding student enrolment in these language courses: 1. No student is enrolled in both French and Chinese courses simultaneously.2. A total of 280 students are enrolled in exactly two languages.3. The number of students enrolled exclusively in French, German, or Spanish courses is 10 for each language.4. The numbers of students not enrolled in French, German, and Spanish courses are in the ratio of 5 : 3 : 2, respectively.5. There are 60 students enrolled in the Chinese course, and all of these students are also enrolled in exactly two other languages.Question 14How many students are enrolled in the Spanish language course?

Question

Refer to the data below and answer the questions that follow.Super 100 Language Academy offers courses in four foreign languages: French, German, Spanish, and Chinese, serving a total of 400 students. Each student is enrolled in at least one language course and may be enrolled in multiple courses. The following are specifics regarding student enrolment in these language courses: 1. No student is enrolled in both French and Chinese courses simultaneously.2. A total of 280 students are enrolled in exactly two languages.3. The number of students enrolled exclusively in French, German, or Spanish courses is 10 for each language.4. The numbers of students not enrolled in French, German, and Spanish courses are in the ratio of 5 : 3 : 2, respectively.5. There are 60 students enrolled in the Chinese course, and all of these students are also enrolled in exactly two other languages.Question 14How many students are enrolled in the Spanish language course?

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Solution

To determine the number of students enrolled in the Spanish language course, we need to analyze the given data step by step.

  1. Total Students: 400 students.

  2. Students enrolled in exactly two languages: 280 students.

  3. Students enrolled exclusively in French, German, or Spanish: 10 students each for French, German, and Spanish.

    • Therefore, students enrolled exclusively in one language = 10 (French) + 10 (German) + 10 (Spanish) = 30 students.

  4. Students not enrolled in French, German, and Spanish: The ratio is 5:3:2.

    • Let the number of students not enrolled in French be 5x5x.
    • Let the number of students not enrolled in German be 3x3x.
    • Let the number of students not enrolled in Spanish be 2x2x.

  5. Students enrolled in Chinese: 60 students, and all are enrolled in exactly two other languages.

  6. No student is enrolled in both French and Chinese simultaneously.

Let's break it down further:

Step-by-Step Calculation:

  1. Determine xx:

    • The total number of students not enrolled in French, German, and Spanish is 5x+3x+2x=10x5x + 3x + 2x = 10x.
    • These students are part of the 400 total students.
    • Since 60 students are enrolled in Chinese and all are enrolled in exactly two other languages, they are not part of the exclusive language students.
    • Therefore, 10x=6010x = 60 (since these 60 students are not enrolled in French, German, or Spanish exclusively).

    Solving for xx: 10x=60  ⟹  x=6 10x = 60 \implies x = 6

  2. Number of students not enrolled in each language:

    • Not enrolled in French: 5x=5×6=305x = 5 \times 6 = 30
    • Not enrolled in German: 3x=3×6=183x = 3 \times 6 = 18
    • Not enrolled in Spanish: 2x=2×6=122x = 2 \times 6 = 12

  3. Students enrolled in each language:

    • Total students = 400.
    • Students not enrolled in French = 30, so students enrolled in French = 400 - 30 = 370.
    • Students not enrolled in German = 18, so students enrolled in German = 400 - 18 = 382.
    • Students not enrolled in Spanish = 12, so students enrolled in Spanish = 400 - 12 = 388.

Conclusion:

The number of students enrolled in the Spanish language course is 388.

This problem has been solved

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