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?
With venn diagram, i came up with these equations.
(F- F/5) + (S - S/7) = 110; and F/5 = S/7
11 students took both courses
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…
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