Thirty percent of all the students in a school are in a play. All students except for 140 are In the play.
How many students are in the school?
Tutors, please sign in to answer this question.
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)
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
x=total number of students
Let's subtract x from both sides...
Let's divide both sides by -0.70
30% of 200=0.30(200)=60 students in play
140 are exceptions who are not in play.