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A company that specializes in language tutoring lists the following information concerning its English-speaking employees: 23 employees speak German; 29 speak French; 33 speak Spanish; 43 speak Spanish or French; 38 speak French or German; 48 speak German or Spanish; 8 speak Spanish, French, and German; and 7 speak English only. (Round your answer to one decimal place.)

(a) What percent of the employees speak at least one language other than English?


(b) What percent of the employees speak at least two languages other than English?

Respuesta :

mathmate
I assume the sentences:
"23 employees speak German; 29 speak French; 33 speak Spanish"
mean these speak ONLY the respective languages other than English.
Then the calculations boil down to those who speak ONLY two languages, noting that 8 speak French, German and Spanish, which need to be subtracted from 
1. French and Spanish: 43-8=35 (speak only two foreign languages)
2. German and French: 38-8=30 (speak only two foreign languages)
3. German and Spanish: 48-8=40 (speak only two foreign languages).

Now We add up the total number of employees:
zero foreign language = 7
one foreign language  = 23+29+33=85
two foreign languages = 30+35+40=105
three foreign languages=8
Total =7+85+105+8=205

(a) Percentage of employees who speak at least one foreign lanugage = (85+105+8)/205=198/205=.966=96.6%
(b) Percentage of employees who speak at least two foreign lanugages = (105+8)/205=113/205=.551=55.1%

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