SOLUTION: 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 l

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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 l      Log On


   

Question 170208This question is from textbook A Problem Solving Approach to Mathematics for Elementary School Teachers
: 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 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 Sum have This question is from textbook A Problem Solving Approach to Mathematics for Elementary School Teachers

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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All of them study either 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 Sum have
:
Let x = no. of students he has
:
"One-half of them study languages only,
.1%2F2x
" one-fourth of them study French,"
1%2F4x
:
" one-seventh of them study physics only,"
1%2F7x
and 20 do not study at all.” How many students does Professor Sum have
:
The French students are included with the languages, so we have:
x = 1%2F2x + 1%2F7x + 20
Multiply equation by 14
14x = 7x + 2x + 280
:
14x - 9x = 280
x = 280%2F5
x = 56 students