Of the 80 students in class, 25 are studying German, 15 French and
13 Spanish. 3 are studying German and French; 4 are studying French and
Spanish; 2 are studying German and Spanish; and none is studying all 3
languages at the same time. How many students are not studying any of
the three languages?
German only = 25 - 3 -2 = 20
French only = 15 - 3 - 4 = 8
Spanish only = 13 - 2 - 4 = 7
combos = 3 +2 + 4 = 9
onlys +combos = 44
80 - 44 = 36
36
Well, it seems like these students are really trying to avoid any language barriers! Let's break it down, shall we?
We start with the total number of students, which is 80. Now, let's calculate:
25 students are studying German,
15 students are studying French,
13 students are studying Spanish.
We know that 3 students are studying both German and French, 4 students are studying both French and Spanish, and 2 students are studying both German and Spanish. Hmm, it's like a language love triangle!
But hold on, none of them are studying all three languages at the same time! So we have to subtract these "language lovers" from the total number of students considering the overlaps.
If we add up the unique numbers, we get: 25 (German) + 15 (French) + 13 (Spanish) = 53.
Now, let's subtract the overlaps:
53 - 3 (German & French) - 4 (French & Spanish) - 2 (German & Spanish) = 44.
Voila! There are 44 students who are studying at least one of the three languages. But, wait for it...
We're not done yet! You asked how many students are not studying any of the three languages. So, let's subtract this from the total number of students:
80 (total) - 44 (studying at least one language) = 36.
So, it seems like 36 students are clowning around and not studying any of the three languages. Maybe they're preparing to join the circus instead!
To find the number of students who are not studying any of the three languages, we need to subtract the number of students studying at least one language from the total number of students.
Let's break down the information given:
- The number of students studying German = 25
- The number of students studying French = 15
- The number of students studying Spanish = 13
- The number of students studying German and French = 3
- The number of students studying French and Spanish = 4
- The number of students studying German and Spanish = 2
- None of the students are studying all 3 languages at the same time.
To find the number of students studying at least one language, we can add up the number of students studying each language separately:
Total number of students studying at least one language = Students studying German + Students studying French + Students studying Spanish
Total number of students studying at least one language = 25 + 15 + 13 = 53
Now, we can find the number of students not studying any of the three languages by subtracting the number of students studying at least one language from the total number of students:
Number of students not studying any of the three languages = Total number of students - Number of students studying at least one language
Number of students not studying any of the three languages = 80 - 53 = 27
So, there are 27 students who are not studying any of the three languages.