help with mathhh?

Question

A total of 600 tickets were sold for a concert. Twice as many tickets were sold in advance than were sold at the door. If the tickets sold in advance cost $25 each and the tickets sold at the door cost $32 each, how much money was collected for the concert?

and

The owner of a movie theater was counting the money from one day's ticket sales. He knew that a total of 150 tickets were sold. Adult tickets cost $7.50 each and children's tickets cost $4.75 each. If the total receipts for the day were $891.25, how many of each kind of ticket were sold?

?? adult tickets and ?? children's tickets were sold.

Answer 1

400 sold in advance, 200 at the door.
400 ($25) + 200 ($32) = 10000 + 6400 = $16400

A + C = 150
A ($7.50) + C ( $4.75) = $891.25
solve simultaneous equations by substitution:

A = 150 - C
(150 - C) ($7.50) + C ($4.75) = $891.25
1125 -7.5 C + 4.75C = 891.25
1125 - 2.75C = 891.25
-2.75C = - 233.75
C = 85
A = 150 - 85 = 65

Answer 2

These are both solved by writing algebraic equations.
#1
Let a = tickets sold in advance.
let d - tickets sold at the door

so income from advance tickets = 25 times a or 25a
income from door = 32 times d or 32d

and twice as many advance tickets as door sales means;
a = 2d

since total number of tickets = 600 then a + d = 600
let total collected = C and C = 25a + 32d

Now you have 3 equations;
1) C = 25a + 32d
2) a + d = 600
3) a = 2d

Substitute a into one of them (the second one) for its equivalent as expressed in a = 2d

(2d) + d = 600
3d = 600
3d/3 = 600/3
d = 200

Now put his value back into the second equation;
a + d = 600
a + 200 = 600
a + 200 - 200 = 600 - 200
a = 400

Now that you know how many of each ticket typw were sold put these values into your first equation;
C = 25a + 32d
C = (25 x 400) + (32 x 200)

et voila

#2
a = number of adult tickets
c = number of children's tickets

total tickets sold = 150
a + c = 150

total receipts = 891.25
total receipts = income from adult tickets plus income from children's tickets
891.25 = 7.50a + 4.75c

So;
a + c = 150
891.25 = 7.50a + 4.75c

Start by converting a + c = 150 to the form a = ? - ?
and then substitute a into the other equation and you're on your way.
I'll leave you to finish it.
Good luck

:)

Answer 3

let x be the number of tickets sold at the door
2x+x = 600
x = 200

total cost = 400*25 + 200*32 =16400

let x = adult and y = children ticket
x+y = 150
7.50x + 4.75y = 891.25

7.50x + 4.75(150-x) =891.25
750x + 475(150-x) = 89125
275x = 17875
x = 65
y=85

Answer 4

let a= advanced tickets
let d = tickets at door
a+d=600
a=2d
so there fore 2d+d=300
3d=600
d=200
a=400
25(400)+32(200) =$16,400

let a= adult tickets
let c= child tickets
a+c=150 so a=150-c
7.5a+4.75c=891.25
7.5(150-c)+4.75c=891.25
-2.75c=-233.75
c=85
a=65