Math question help......Please explain step by step with an equation and variables....?

Question

Tickets to a concert that were purchased in advance cost $4.50 each, and tickets purchased at the box office on the day of the concert cost $8.00 each. The total amount of money collected in ticket sales was the same as if each ticket purchased had cost $6.00. If 180 tickets were purchased in advance what was the total number of tickets purchased for the concert?

Answer 1

Let t be total number of tckets purchased

Then (t - 180) tickets were purchased on the day as 180 were purchased in afvance

Therefore
Total revenue ($) = 180 x 4.50 + (t - 180) x 8
and this is equivalent to t x 6

ie 810 + 8t - 1440 = 6t (using the distributive law)
On simplifying
8t - 630 = 6t
So
2t - 830 = 0 (on subtracting 6t from both sides)
Therefore
2t = 630
and so
t = 315 (on dividing both sides by 2)

So total tickets sold = 315

Check:
6 x 315 = 1890 So total revenue = $1890

If 180 tickets were presold then (315 - 180) tickets were sold on the day ie 135

So sales = 180 x $4.50 + 135 x $8
= $810 + $1080
= $1890

Yes this balances!!!!

Answer 2

advance tickets = 180, let the box office tickets as z, then
total tickets purchased is 180 + z
4.5$ x 180 + 8$ x z = 6 ( 180 + z )
810 + 8z = 1080 + 6z
2z = 270
z = 135
total tickets = 180 + 135 = 315

Answer 3

so 4.5 = cost of ticket purchased in advance (x)
8.0 = cost of ticket purchased at show (y)

4.5x + 8.0y = 6.0(x+y)

The problem states that if the tickets all cost six dollars, then it would equal the cost of the tickets purchased early (x) and at the show (y).

So...
Using the distributive property we can factor the right side
4.5(180) + 8.0y = 6.0(180) + 6.0y

Then

2.0y = 1.5(180)

2.0y = 270

y = 135

x + y = Total Tickets

180 + 135 = 315

Thus Total Tickets purchased = 315

Answer 4

Ok Here we go:

Assume 'x' to be the total number of tickets sold.
Tickets sold in advance = 180
So Total tickets sold on the day of concert = x - 180

Total amount of money collected in ticket sales = x times $6.00
Total amount of money collected in ticket sales = x X $6.00
Total amount of money collected in ticket sales = 6x

Cost of 180 ticketc sold in advance = 180 X $4.50 = 810

Cost of tickets sold on the day of concert =$8(x - 180)
Cost of tickets sold on the day of concert =8x -1440

So here is the final equation:

Cost of 180 ticketc sold in advance + Cost of tickets sold on the day of concert = Total amount of money collected in ticket sales

810 + 8x -1440 = 6x
8x - 6x = 1440 - 810
2x = 630
x = 630 / 2
x= 315

So total number of tickets sold or purchsed = 315 (Answer)

Hope that helps !

eNwe
for eNwe Studio

Answer 5

Let total no of tickets sold =x
Then according to question
6x=4.50*180+8*(x-180)
6x=810+8x-1440
8x-6x=1440-810
2x=630
x=315

Answer 6

Let the number of advanced tickets purchased= x
Let the number of on the day tickets purchased=y
Total money collected=4.5x+8y
Which is equal to 6(x+y)
ie. 4.5x+8y=6x+6y
1.5x=2y
But x=180
1.5*180=2y
y=135

total number of tickets purchased=135+180
= 315

Answer 7

let x number be purchased at the box office
the equation
=180(4.50)+x*8=(180+x)*6
=810+8x=1080+6x
adding -6x
810+2x=1080
adding -810
2x=270
dividing by 2
x=135
check
810+1080=315*6
checks

Answer 8

x advance purchase
y box office
x=180
z=4.5x + 8y; z=4.5(180) +8y; z= 810 + 8y
z/(x+y)= 6
z=6(x+y); z=6x + 6y; z=6(180) +6y; z=1080+6y

810 +8y = 1080+6y; 8y -6y =1080 - 810; y(8-6) = 270; 2y = 270

y=270/2

y = 135

total tickets sold = x+y ;

total= 180+135= 315

z = 4.5(180) + 8(135); z=810+1080; z=1890

z = 6 (180 + 135); z =6(315) ; z = 1890

Answer 9

a=advance sales=180
b=box office

4.5*180+8b=6(180+b)
810+8b=1080+6b
2b=270
b=135
135+180=315 total tickets.

check
135*8+180*4.5=1080+810=1890
1890/315=6