When Professor Sum was asked by Mr. Little how many students were in his classes, he answered, "All of them study either languages, physics, or not at all. One half of them study lanuages only, one fourth of them study French, one seventh of them study physics only, and 20 do not study at all." How many students does professor sum have?
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How many students does professor sum have?
- Thread starter Kaycee
- Start date
The way I read that:Kaycee said:When Professor Sum was asked by Mr. Little how many students were in his classes, he answered, "All of them study either languages, physics, or not at all. One half of them study lanuages only, one fourth of them study French, one seventh of them study physics only, and 20 do not study at all." How many students does professor sum have?
1/2 study languages (1/4 study French is irrelevant)
1/7 study physics
14/14 - 7/14 - 2/14 = 5/14 study nothing
20/(5/14) = 56 = students
Hello, Kaycee!
Here's my approach . . .
Here's my approach . . .
These must total \(\displaystyle N\), the number of students in the class: .\(\displaystyle \L\frac{N}{2}\,+\,\frac{N}{7}\,+\,20\:=\:N\)When Professor Sum was asked by Mr. Little how many students were in his classes, he answered,
"All of them study either languages, physics, or not at all. . \(\displaystyle \text{Let }N\text{ = number of students}\)
One half of them study lanuages only, . \(\displaystyle \frac{N}{2}\text{ = language}\)
one seventh of them study physics only, . \(\displaystyle \frac{N}{7}\text{ = physics}\)
and 20 do not study at all." . \(\displaystyle 20\text{ = "others"}\)
How many students does professor Sum have?