Question 175235: When professor Sum was asked be Mr. Little how many students were in his classes, he answered, "All of them study languages, physics, or not at all. One-half of them study languages 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 Sam have?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! x = number of students who study language only.
y = number of students who study physics only.
z = number of students who do not study at all.
t = total number of students.
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x + y + z = t
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1/2 of the total study languages only,
so:
x = t/2
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1/4 of the total study french.
since french is a language, this is extraneous information not needed.
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1/7 of the total study physics only,
so:
y = t/7
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20 do not study at all,
so:
z = 20
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substituting in the original equation of:
x + y + z = t, we get:
t/2 + t/7 + 20 = t
multiply both sides of the equation by 14 to get:
7t + 2t + 280 = 14t
combine like terms to get:
9t + 280 = 14t
subtract 9t from both sides of the equation to get:
280 = 5t
divide both sides of the equation by 5 to get:
t = 56
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total number of students is 56.
1/2 study languages = 28.
1/7 study physics = 8
20 don't study at all = 20
total = 28 + 8 + 20 = 56
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