the drama club sold 1500 tickets for the end of the year performance. admission prices were $12 for adults adn $6 for students. The total amount collected at the box office was $16200. How many students attended the play?
2007-01-01 12:40:36 · 8 answers · asked by Hot_Chick 2 in Science & Mathematics ➔ Mathematics
a = # of adult tickets
s = # of student tickets
a + s = 1500
12a + 6s = 16200
Now use a system of equations to solve.
1. Isolate one of the variables.
a + s = 1500
a = 1500 - s
2. Plug this in the other equation.
12a + 6s = 16200
12(1500 - s) + 6s = 16200
3. Solve.
18000 - 12s + 6s = 16200
18000 - 6s = 16200
18000 - 16200 = 6s
1800 = 6s
300 = s
You're done, since the question only asked for 's'.
300 students attended the play.
Hope that helps!
2007-01-01 12:47:21 · answer #1 · answered by teekshi33 4 · 0⤊ 0⤋
Let a = adults, s = students.
Since the drama club sold 1500 tickets, then the tickets must have been sold to some number of adults and some number of students. Therefore
a + s = 1500
Since the total amount collected at the box office was $16200, where tickets were $12 for adults and $6 for students, it follows that
12a + 6s = 16200
Two equations, two unknowns:
a + s = 1500
12a + 6s = 16200
To solve this system of equations, use substitution. Since
a + s = 1500, then a = 1500 - s. Plug in this value of a into the second equation.
12(1500 - s) + 6s = 16200
Now, solve it normally for s.
18000 - 12s + 6s = 16200
18000 - 6s = 16200
-6s = -1800, so
s = 300
300 students attended the play.
2007-01-01 12:46:08 · answer #2 · answered by Puggy 7 · 0⤊ 0⤋
Let a = # of adults and s = # of students
1500 = a + s
16200 = 12a + 6s
Multiply the first equation by -12 (addition method)
-18000 = -12a -12s (add this to the second equation)
16200-18000 = -6s
-1800 = -6s
s=300 students
2007-01-01 12:47:51 · answer #3 · answered by Professor Maddie 4 · 0⤊ 0⤋
12*X + 6*Y = 16200
X + Y = 1500
Y = 1500 - X
12*X + 6 * ( 1500 - X ) = 16200
12X -6X + 9000 = 16200
6X = 7200
X = 1200
Y = 300
2007-01-01 12:45:42 · answer #4 · answered by TankAnswer 4 · 0⤊ 0⤋
12x + 6y = 16200
x + y = 1500
12x - 6x + 6y - 6y = 16200 - 9000
6x = 7200
x = 1200
y = 300
2007-01-01 12:45:47 · answer #5 · answered by Modus Operandi 6 · 0⤊ 0⤋
6x + 12(1500-x) = 16200
6x -12x + 18000 = 16200
6x = 1800
x = 300 students
2007-01-01 12:44:58 · answer #6 · answered by Anonymous · 0⤊ 0⤋
a=adults
c=students
a+c=1500
12a+6c=16200
a=1500-c
sub into other equation
and you get
12(1500-c)+6c=16200
18000-12c+6c=16200
-12c+6c=-1800
-6c=-1800
number of children there(c)=300
2007-01-01 12:47:54 · answer #7 · answered by cajazzbat 2 · 0⤊ 0⤋
900 students
2007-01-01 12:50:09 · answer #8 · answered by Kurtizz 1 · 0⤊ 0⤋