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KCC's Quizzes: University Elective Courses

In a university, students might (if they want to) take up to 2 optional foreign language courses: French or Spanish.

1/5 of the students who take French, also take Spanish.

1/7 of the students who take Spanish, also take French.

110 students take only one course.

We assume the two courses are not occurring on the same date.

Question: How many students take both courses?

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Parents
  • Suppose F = Number of students who take French; S = Number of students who take Spanish.

    F-F/5 = students who only take French; S-S/7 = students who only take spanish

    (F-F/5) + (S-S/7) = 110

    We know that F/5 = S/7; therefore we can get F in terms of S or S in terms of F.
    F = 5S/7

    (5S/7 - S/7) + (S-S/7) = 110 therefore S = 77

    S/7 = 77/7 = 11

    11 students take both courses

Reply
  • Suppose F = Number of students who take French; S = Number of students who take Spanish.

    F-F/5 = students who only take French; S-S/7 = students who only take spanish

    (F-F/5) + (S-S/7) = 110

    We know that F/5 = S/7; therefore we can get F in terms of S or S in terms of F.
    F = 5S/7

    (5S/7 - S/7) + (S-S/7) = 110 therefore S = 77

    S/7 = 77/7 = 11

    11 students take both courses

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