Question

You are selling tickets for a musical at your school. Student tickets cost $5 and adult tickets cost $8.

If you sell 500 tickets and collect $3475, how many student tickets and how many adult tickets did you sell?

Answer 1

We can express all the facts with 2 equations in 2 unknowns.

Let A be number of adult tickets. Sales of adult tickets will generate 8A dollars.
Let S be number of student tickets. Sales of student tickets will generate 5S dollars

Adult tickets sold + student tickets sold add up to 500, so \(A+S = 500\)
Adult ticket revenue + student ticket revenue adds up to $3475, so \(8A + 5S = 3475\)

Can you solve that system of equations?

Answer 2

As the first equation easily gives you A or S in terms of the other, substituting one in place of the other in the second equation would work. Or you could use elimination.

Answer 3

You could even do a "guess and check" approach of assuming all of the tickets sold were student tickets, which would earn 5*500 = 2500 dollars. That's shy of the total you need by 3475-2500 = 975. If trading 1 student ticket for 1 adult ticket increases your revenue by 8-5 = 3 dollars, how many student tickets would have to be exchanged for adult tickets to make up 975 dollars?

Answer 4

i got it ! thank you :))

Answer 5

what did you get for your answer?

Answer 6

325 student and 175 adult

Answer 7

oh, let's check that:

325* 5 + 175* 8 = ?

Answer 8

3025...

Answer 9

yeah, that isn't 3475, is it? perhaps you've swapped your labels:

325*8 + 175*5 =

Answer 10

oh..i get it, i didn't think to check it like that.. the answer is 3475

Answer 11

Right. Moral of the story: after you've written down your final answer, go back and plug in the answer and make sure it truly solves the problem.

Answer 12

lol that's something i need to work on. Thank you so much :)

Answer 13

it's easy to switch things around like this, or to discover upon rereading the question that you didn't understand it quite correctly, etc.

Answer 14

I hate having people point out that I make mistakes, and I know I make mistakes, so I always check my answers :-)

Answer 15

and you may discover patterns in how you make mistakes, which you can work to overcome. I know that subtracting polynomials is something that often trips me up, so I try to avoid doing that by adding (after changing signs) instead of subtracting.

Answer 16

anyhow, good luck! don't get caught skimming off the ticket revenues :-)

Answer 17

lol thanks :)