SOLUTION: The attendance at a ball game was 400 people. Student tickets cost $2 and adult tickets cost $3. If $1050 was collected in ticket sales, how many of each type of ticket was sold?

Question 158550: The attendance at a ball game was 400 people. Student tickets cost $2 and adult tickets cost $3. If $1050 was collected in ticket sales, how many of each type of ticket was sold?
Found 2 solutions by gonzo, nerdybill:
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
let a = number of tickets sold to adults
let s = number of tickets sold to students
total tickets sold were 400
formula for number of number of tickets sold to adults and number of tickets sold to students becomes
a+s = 400 (first equation)
cost per adult ticket is $3.00
cost per student ticket is $2.00.
total revenue is $1050
formula for revenue from students and adults is
($3 * a) + ($2 * s) = $1050 (second equation)
to remove one of the unknowns from the second equation, we go to the first equation and solve for one of the unknowns in terms of the other.
from the first equation
a+s=400
which becomes
a=400-s
which means we have determined the number of adult tickets in terms of the number of student tickets
substituting a = 400 - s in the second equation, we get
($3 * (400-s) + ($2 * s) = $1050
this becomes
$1200 - ($3 * s) + ($2 * s) = $1050
this becomes
$1200 - ($1 * s) = $1050
this becomes
$1200 - $1050 = $1*s
which becomes
s = ($1200 - $1050)/$1
which becomes
s = 150
number of students is 150.
number of adults is 400 - 150 = 250.
substituting in the equation for the money (second equation), we get
150 * $2 + 250 * $3 = $1050
$300 + $750 = $1050
$1050 = $1050
formula is correct.
number of tickets sold to students = 150
number of tickets sold to adults is 250.

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The attendance at a ball game was 400 people. Student tickets cost $2 and adult tickets cost $3. If $1050 was collected in ticket sales, how many of each type of ticket was sold?
.
Let x = number of $2 tickets sold
then because there was a total of 400 people
400-x = number of $3 tickets sold
.
If total collected was $1050:
2x + 3(400-x) = 1050
2x + 1200 - 3x = 1050
1200 - x = 1050
1200 = x+1050
150 = x (number of $2 tickets sold)
.
$3 tickets sold:
400-x = 400-150 = 250 (number of $3 tickets sold)

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