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The table shown lists the distribution of a certain number of humaniti
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12 Aug 2025, 23:57
12 Aug 2025, 23:57
Expert Reply
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Question Stats:
50% (02:08) correct
50% (00:57) wrong based on 4 sessions
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The table shown lists the distribution of a certain number of humanities students by major. Which of the following could be the total number of students if at least 190 students are History majors?
Indicate all such numbers.
A) 900
B) 904
C) 905
D) 950
E) 1000
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Re: The table shown lists the distribution of a certain number of humaniti
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23 Aug 2025, 10:48
23 Aug 2025, 10:48
Expert Reply
In order to solve this problem, we can set up an equation.
First, we know that History majors account for \(21\)% of the total number of students.
We also know that we want $\(21\) %$ to equal at least 190 students.
This equation will yield the smallest possible number of students needed for 190 to equal \(21\)%:
$$
\(\begin{aligned}
\frac{21}{100} & =\frac{190}{x} \\
21 x & =19,000 \\
x & =904.76
\end{aligned}\)
$$
Since we cannot have .76 of a person, we round up to 905 : this is the lowest possible total number of students for $\(21\) %$ to equal at least 190 students. Thus, any total equal to or greater than 905 works.
This means that (C), (D), and (E) are our answers.
First, we know that History majors account for \(21\)% of the total number of students.
We also know that we want $\(21\) %$ to equal at least 190 students.
This equation will yield the smallest possible number of students needed for 190 to equal \(21\)%:
$$
\(\begin{aligned}
\frac{21}{100} & =\frac{190}{x} \\
21 x & =19,000 \\
x & =904.76
\end{aligned}\)
$$
Since we cannot have .76 of a person, we round up to 905 : this is the lowest possible total number of students for $\(21\) %$ to equal at least 190 students. Thus, any total equal to or greater than 905 works.
This means that (C), (D), and (E) are our answers.
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