Two types of tickets are sold for a concert. Adult tickets cost $12 each, while student tickets each cost $8. A total of 322 tickets are sold, bringing in a total of $3,456. How many students tickets were sold?
2007-07-06 11:16:55 · 11 answers · asked by *05* 1 in Science & Mathematics ➔ Mathematics
Let x be the number of student tickets sold.
Then 322-x is the number of adult tickets sold.
3456=8x + 12(322-x) Multiply the 12 through to get
3456=8x + 3864 - 12x Subtract 3864 from both sides
3456 - 3864 = -4x (subtract and divide both sides by -4 to get
-408/-4 = x (simplify)
102 = x
There were 102 Student tickets sold.
2007-07-06 11:28:14 · answer #1 · answered by Jason K 2 · 0⤊ 0⤋
Let A be the number of adult tickets sold and S be the number of student tickets sold.
Also recall that (unit price)*(number of item sold) = total price
12A + 8S = 3456
A + S = 322
S = 322 - A
12A + 8(322 - A) = 3456
12A + 2576 - 8A = 3456
4A = 880
A = 220
(220) + S = 322
S = 102
2007-07-06 11:22:18 · answer #2 · answered by whitesox09 7 · 2⤊ 0⤋
You will need to do this as a system of equations. Let's call "x" the number of adult tickets purchased and "y" the number of student tickets purchased.
From the word problem, we see:
$12x + $8y= $3,456
x + y = 322
Now we simplify for x:
x= 322- y
Then, we substitute this value into the other equation:
$12 (322- y)+ $8y= $3,456
Simplify and solve:
3,864 - 12y + 8y = 3,456
-12y + 8y = -408
-4y = -408
y = 102 tickets
x + y = 322
x = 102= 322
x= 220 tickets
Then, check to be sure it is correct:
$12 (220) + $8 (102) = $3,456
$2,640 + $816 = $3,456
$3,456= $3,456
So, this is correct!
2007-07-06 11:26:50 · answer #3 · answered by bradbury 2 · 1⤊ 0⤋
Let's see,
s= student tickets
a=adult tickets
s+a= 322
8s+12a=3456
Solving two equations in two unknowns,
s= 322-a
8(322-a) + 12a = 3456
2576 - 8a + 12a = 3456
4a = 3456 - 2576
4a = 880
a = 220 Adults tickets sold
s = 322 - 220 = 102 Student Tickets sold
2007-07-06 11:26:22 · answer #4 · answered by alrivera_1 4 · 0⤊ 0⤋
let x = no. of tickets sold to students
322- x = no. of tickets sold to adults
$12 x + $8 (322- x) = $3456
$12 x + $2576 - $8 x = $3456
$4 x = $880
x = 220 tickets sold to students
322- x =102 tickets sold to adults
2007-07-06 11:29:12 · answer #5 · answered by CPUcate 6 · 0⤊ 0⤋
Let s be the number of students.
Then there were 322 - s adults.
12(322 - s)+ 8s = 3456
3864 - 4s = 3456
4s = 408
s = 102
There were 102 student tickets sold.
2007-07-06 11:23:24 · answer #6 · answered by Anonymous · 3⤊ 0⤋
Let x be adult tickets.
Since 322 are sold, 322-x are student tickets.
Proceeds = SUM (tickets * price/ticket)
3456 = 12 * x + 8 (322-x)
Solve. 322-x is your answer.
2007-07-06 11:24:00 · answer #7 · answered by cattbarf 7 · 1⤊ 0⤋
Let x be the number of adult tickets.
Let y be the number of student tickets.
x + y = 322 => 8x + 8y = 2576 ----(1)
12x + 8y = 3456 ----(2)
(2)-(1): 4x = 880 => x = 220
220 + y = 322
y = 102
2007-07-06 11:35:45 · answer #8 · answered by Kemmy 6 · 0⤊ 0⤋
102
2007-07-06 11:44:47 · answer #9 · answered by Corey 2 · 0⤊ 1⤋
form simultaneous equations like this:
12x + 8y = 3456
x + y = 322
x is the number of adult tickets and y the no of student tickets.
I hope that makes sense and gets you started, I'm not going to do all of your homework.
2007-07-06 11:24:45 · answer #10 · answered by Anonymous · 1⤊ 0⤋