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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?

• 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

• In order to not influence the still coming answers, I will comment the feedback only in a week together with the "official" and detailed response! Please don't hesitate to jump on it; there will be still the 4 first winners announced!

Kuo-Chang

• It is my first time here on Engineer Zone, is there a "Spoiler" tag similar to forums?
That way we can hide our answers to other reader as well?

• `Trying Out HTML Code`
```<details>
<summary>Details</summary>
Something small enough to escape casual notice.
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Trying white  Looks like like we can set background to black then highlight it to see what's written or just CTRL+A to reveal everything

• 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

• Additional info : the ones who also prefer not to influence others, they can still send their detailed answer to my email:

kuo-chang.chan@analog.com

If so, I can comment the feedback 1:1 immediately (also by email)

Regards

Kuo-Chang

• Mmmm, are you sure Manikandan? If you can, I am curious to see the reasoning you made (you can send it to my email address kuo-chang.chan@analog.com

• Answer is 11.  Here is my logic……..

• If 55 students take French, then 11 students take Spanish leaving 44 students with French only.

• If 77 students take Spanish, then 11 students take French leaving 66 students with Spanish only.

• Thus 110 students take only 1 course.
• Thanks Jeff!