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How many students are in the school?

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4 Answers

Let x = the total number of students, and p = number of students in the play.
 
If 30 percent of students are in the play:
.3x = p
 
If All except for 140 are in the play:
x - 140 = p
 
Now we have 2 equations, so use substitution to solve for x:
x - 140 = .3x
x - .3x = 140
.7x = 140
x = 140 / .7 = 200
 
Now that we know x, solve for p:
200 - 140 = p
60 = p
 
There are 200 students total, and 60 in the play.
30% are in the play
70% are not in the play
140 are not in the play
140 is 70% of total # of students(call this n)
140=70%*n
140=0.7n
1400=7n
1400/7=n
200=n
 
What you know:  30% of all students in play & 140 students not in the play
What you need to know:  # of students in school
 
Formulas:  Total Students in School x % in play = # students in play 
  Students in play + Students not in play = Total Students in School
 
If you merge the two formulas you get:  Total Students in School = (Total Students x % in play) + students not in play.
 
Plug in the numbers:  Total Students = (Total Students x 30%) + 140 -or-    x=.30x+140
 
Solve for x:
Subtract 0.30x from both sides:  x-.3x = 140 -or- .7x = 140
Divide both sides by .7:  0.7x / 0.7 = 140 / 0.7
You get x = 200.  So there are 200 students in the school
 
Hi Travina;
30%=0.30
x=total number of students
(0.30)x=x-140
Let's subtract x from both sides...
-x+(0.30)x=-140
-(0.70x)=-140
Let's divide both sides by -0.70
-(0.70x)/(-0.70)=-140/(-0.70)
x=200
 
30% of 200=0.30(200)=60 students in play
140 are exceptions who are not in play.
60+140=200