Question

MATH EXAM TOMORROW HELP MEDAL AND FAN
Tickets for a popular rock concert where sold out for an auditorium that has 8000 seats. The premium seat tickets sell for 50 and regular seats are 30. If the total revenue generated from sales was 250,00, determine the number of tickets were sold at each price.

Answer 1

need 2 linear equations to solve this problem

Answer 2

Let p be the number of premium seat tickets sold, and r be the number of regular seat tickets sold. What two equations can we set up?

Answer 3

idk

Answer 4

Okay, no worries. So we know 8000 total tickets were sold, right?

Answer 5

that why Im asking you lol

Answer 6

can you just show me how you do it please?

Answer 7

Yeah I can explain it. So we know 8000 total tickets were sold, so that means the number of premium seat tickets and regular seat tickets combined have to be 8000, right?

Answer 8

k

Answer 9

So, since we let p be the number of premium seat tickets, and r be the number of regular seat tickets, we can set up the first equation
\[p + r = 8000\]

Answer 10

ok

Answer 11

Now, we look at the revenue gained. The total revenue gained was 250,000. So we know that this total comes from the price of each ticket multiplied by their respective price combined. Since the premium seat tickets cost 50 and the regular seat tickets cost 30, we can set up the second equation
\[50p + 30r = 250,000\]

Answer 12

Does that make sense?

Answer 13

I made a mistake above in what I said. I meant to say that the total revenue gained comes from the price of each ticket multiplied by the number of those tickets all combined.

Answer 14

it makes sesne but how do i solve the problem with these equations?

Answer 15

Okay so we have the equations
\[p + r = 8000\]
and
\[50p + 30r = 250,000\]
now we can take the first equation and rearrange the variables to get
\[p = 8000-r\]
right?

Answer 16

just do it please

Answer 17

I am, I'm just trying to walk you through it as well.

So now that we have an equation that is solved for p, we can substitute it into the second equation to get
\[50[8000-r] + 30r = 250,000\]
and then just solve for r, and you'll get a number that you can put into the first equation and solve for p, and you'll have the answer.

Answer 18

where di p go?

Answer 19

did*

Answer 20

I used the rearranged first equation
\[p = 8000-r\]
and substituted it for p in the second equation
\[50p + 30r = 250,000\]

Answer 21

got it

Answer 22

Does it all make sense?