Answer:

(31 + 17) - (50 - 10) = 8

or

31 + 17 = 48

50 - 10 = 40

48 - 40 = 8 students who STUDY both French & Spanish.

Examples:

A general tip is to break down a hard problem into smaller easier PROBLEMS. I also get the feeling that you are a lot like me (need to visualize the solution).

First of all, let’s work with smaller numbers to make it easier to both calculate and visualize.

Lets say there are instead 6 students:

3 of these students studies French:  

2 students study Spanish:

So this will be our first simple problem to solve:

Right now we will interpret these parameters as:

3 students study French

2 students study Spanish

3 + 2 = 5 students studies a language

Also, 1 student doesn’t study any language (at least not French or Spanish)

Now when we KNOW the parameters of the first part we can move on to the second part.

Let’s say the question states that there are 2 students that doesn’t study any language.

Well, based on our calculation so far we have said that there should be only 1 student that doesn’t study any language, so let’s see what we need to change to make the equation make sense again.

According to the question there are only 6 students, but we have (3 + 2 = 5) + 2 = 7 students in our calculation, which creates an overlap with 1 student:

So, since there are 2 students that doesn’t doesn’t study anything, and there is an overlap of 1 student, 1 student have to study both French & Spanish.

All you need to do now is to translate the above logic into a mathematical equation:

French + Spanish = Number of students in both the French and the Spanish class

Students - No Language = Number of unique students in both classes

(French + Spanish) - (Students - No Language) = Students who study both languages

3 + 2 = 5 students who study either French or Spanish

6 - 2 = 4 student who study French, Spanish or both

5 - 4 = 1 student who study both French & Spanish

Or:

(3 + 2) - (6 - 2) = 1

Now when we know how to solve it mathematically, just plug in the variables of your question and you will have your answer :)

31 + 17 = 48

50 - 10 = 40

48 - 40 = 8 students who study both French & Spanish

Or:

(31 + 17) - (50 - 10) = 8

Hope it helps you :D