OpenStudy (anonymous):

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?

5 years ago
OpenStudy (whpalmer4):

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?

5 years ago
OpenStudy (whpalmer4):

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.

5 years ago
OpenStudy (whpalmer4):

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?

5 years ago
OpenStudy (anonymous):

i got it ! thank you :))

5 years ago
OpenStudy (whpalmer4):

what did you get for your answer?

5 years ago
OpenStudy (anonymous):

325 student and 175 adult

5 years ago
OpenStudy (whpalmer4):

oh, let's check that: 325* 5 + 175* 8 = ?

5 years ago
OpenStudy (anonymous):

3025...

5 years ago
OpenStudy (whpalmer4):

yeah, that isn't 3475, is it? perhaps you've swapped your labels: 325*8 + 175*5 =

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (whpalmer4):

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.

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (whpalmer4):

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.

5 years ago
OpenStudy (whpalmer4):

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

5 years ago
OpenStudy (whpalmer4):

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.

5 years ago
OpenStudy (whpalmer4):

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

5 years ago
OpenStudy (anonymous):

lol thanks :)

5 years ago