SOLUTION: The Land O� Lakes High School auditorium has exactly 26 rows of seats. The rows are labeled, in order, from the front of the auditorium to the back from A through Z. There are 8 se

Question 1129988: The Land O� Lakes High School auditorium has exactly 26 rows of seats. The rows are labeled, in order, from the front of the auditorium to the back from A through Z. There are 8 seats in the row A. Each row after the first row has two more seats than the previous row. There are 10 seats in row B, 12 seats in row C and so on. How many seats are there in row Z?
For this answer, I have 58 seats.
What is the total number of seats in the Land O� Lakes High School auditorium?
For this answer, I have 1508 seats

Land O� Lakes High School collected $2860 from ticket sales for the winter concert. A ticket was sold for every seat in the auditorium, resulting in a sold out concert. If the price of an adult ticket was three times the price of a student ticket, and twice as many student tickets were sold as adult tickets, what was the price of a student ticket?
I cannot figure out this last one.
Found 3 solutions by Boreal, math_helper, rothauserc:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
sum=(n/2)(2a+(n-1)d)=13(16+(25)(2))=13*66=858 seats
student=x
adult=858-x
x=2(858-x)
3x=1716
x=572 student tickets and 286 adult tickets
student ticket costs y
adult ticket costs 3y
572y+286(3y)=2860
1430y=2860
y=$2, student ticket cost
3y=$6, adult ticket cost
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
Row Z having 58 seats is correct. Good work.

Not sure what you did to find 1508 seats, since you did not show your work. Using (average number of seats per row) x (number of rows): correct total number of seats is ((8 + 58)/2)*26 = 858

For the last part:
let A = number of adult tickets sold
let S = number of student tickets sold

(eq 1) A + S = 858 (a ticket for every seat was sold)
(eq 2) S = 2A
The total ticket sales information will be used later�

Solve to get
A = 286
S = 572

Now, incorporating the total ticket sales:
Let x = price of student ticket, then 3x = price of an adult ticket
2860 = A*(3x) + S*(x)

Plug in for A and S, then solve for x to get the price of a student ticket ($2)

Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
this is an arithmetic sequence
:
x(n) = a +2(n-1)
:
a = 8
:
x(26) = 8 +2(26-1) = 58
:
*****************
58 seats in row Z
*****************
:
use the formula for the sum of the elements of an arithmetic sequence
:
sum = (n/2)*(2a +(n-1)d), where n=26, a=8, d=2
:
sum = (26/2)*(2*8 +(26-1)*2) = 858
:
*************************************
there are 858 seats in the auditorium
*************************************
:
let a be the number of adult tickets, then number of student tickets is 2a
:
1) a +2a = 858
:
3a = 858
:
a = 286
:
286 adult tickets were sold and 572 student tickets were sold
:
let x be the cost of a student ticket, then 3x is the cost of an adult ticket
:
286*(3x) +572x = 2860
:
858x +572x = 2860
:
1430x = 2860
:
x = 2
:
***************************
the student ticket costs $2
***************************
:
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