SOLUTION: At Prime High School there are three language classes; French, German and Mandarin. There are 40 students in each class. 5 students study all three languages. 12 students study o

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Question 1006027: At Prime High School there are three language classes; French, German and Mandarin. There are 40 students in each class.
5 students study all three languages.
12 students study only German and Mandarin.
15 students study only French and Mandarin.
11 students study only French.
How many students study languages at Prime High School?
Please show the work. Thanks.
Answer by MathTherapy(10552) About Me  (Show Source):
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At Prime High School there are three language classes; French, German and Mandarin. There are 40 students in each class.
5 students study all three languages.
12 students study only German and Mandarin.
15 students study only French and Mandarin.
11 students study only French.
How many students study languages at Prime High School?
Please show the work. Thanks.
.

Total in French class: 40

French only: 11

French & Mandarin: 15

All 3: 5

French & German: 40 – (11 + 15 + 5), or 40 – 31, or 9



Total in Mandarin class: 40

Mandarin & German: 12

Mandarin & French: 15

All 3: 5

Mandarin only: 40 – (12 + 15 + 5), or 40 – 32, or 8



Total in German class: 40

German & Mandarin: 12

German & French: 9 

All 3: 5

German only: 40 – (12 + 9 + 5), or 40 – 26, or 14



Number of students who study languages: 11 + 9 + 15 + 5 + 14 + 12 + 8 = highlight_green%2874%29