Tristan W. answered • 06/02/23
Cornell University Engineering Grad | 7+ Years Tutoring Math & Physics
Hey Kat,
The wording throughout this question is a bit tricky... normally the term "or" is interpreted as either one (but not both), while the term "and" is interpreted as both. I am going to assume this standard convention is followed when giving my answer.
Example 1: The phrase "45 speak Spanish or French" indicates that, given this population of 45 workers, a fraction of them speak Spanish and the remainder of them speak French. We don't know how many speak which language, but at least we know that none of them speak both languages listed.
Example 2: The phrase "8 speak Spanish, French, and German" indicates that, given this population of 8 workers, all 8 of them speak both Spanish, French, and German.
Now that we have the terminology defined, we can start addressing the problem. There's important information in the first sentence: "A company that specializes in language tutoring lists the following information concerning its English-speaking employees". What this tells us is that we can assume that all employees listed know English (in addition to any listed languages).
I organized the groups below and added a tally in [brackets] for how many languages each group knows in addition to English:
23 speak German [1 additional language]
29 speak French [1 additional language]
33 speak Spanish [1 additional language]
45 speak Spanish or French [1 additional language]
34 speak French or German [1 additional language]
48 speak German or Spanish [1 additional language]
8 speak Spanish, French, and German [3 additional languages]
7 speak English Only [0 additional languages]
Question (a): What percent of the employees speak at least one language other than English? (Round the answer to one decimal place.)
Answer (a): The equation for percentage is as follows:
Percent = ((# of Parts)/(Total # of Possible Parts))*100%
To find "# of Parts", we need to add up any group whose tally is more than "0" additional languages.
"# of Parts" = 23 + 29 + 33 + 45 + 34 + 48 + 8 = 220
To find "Total # of Possible Parts", we need to add up every single available group, regardless of their tally.
"Total # of Possible Parts" = 23 + 29 + 33 + 45 + 34 + 48 + 8 + 7 = 227
Now we can plug these numbers into our formula: Percent = ((220)/(227))*100% = 96.916...%.
The last step is to round this number to the nearest one decimal place. To do this, we look at the decimal place to the right of it (in this case, the tens decimal place). That number is "1", and since 1 is less than 5, we round down. This gives us 96.9% for our final answer to question (a)!
Question (b): What percent of the employees speak at least two languages other than English? (Round the answer to one decimal place.)
Answer (b): Again, the equation for percentage is as follows:
Percent = ((# of Parts)/(Total # of Possible Parts))*100%
To find "# of Parts", we need to add up any group whose tally is more than "1" additional language.
"# of Parts" = 8
To find "Total # of Possible Parts", we need to add up every single available group, regardless of
their tally.
"Total # of Possible Parts" = 23 + 29 + 33 + 45 + 34 + 48 + 8 + 7 = 227
Now we can plug these numbers into our formula: Percent = ((8)/(227))*100% = 3.524...%.
The last step is to round this number to the nearest one decimal place. To do this, we look at the decimal place to the right of it (in this case, the tens decimal place). That number is "2", and since 2 is less than 5, we round down. This gives us 3.5% for our final answer to question (b)!
Thanks,
Tristan
