Question 281706: so this is the problem,
tickets for a basketball tournament were $6 for students and $9 for nonstudents. Total sales were $10,500, 250 more students tickets were sold than nonstudents. How many of each type of ticket were sold?
this is what I have..
600 non students
850 students
total sales $10,500
I have used every form of math that I can to come up with this answer yet i do not know how to plug it into an algebra equation, can you help?
Found 2 solutions by Greenfinch, PRMath:
Answer by Greenfinch(383)   (Show Source):
You can put this solution on YOUR website! Let non-student sales = X, then student sales are x + 250.
Amount sold is 9X + 6X + 6x250 = 10500
So 15X = 9000
Non student sales are therefore 600
Answer by PRMath(133)  (Show Source):
You can put this solution on YOUR website! tickets for a basketball tournament were $6 for students and $9 for nonstudents. Total sales were $10,500, 250 more students tickets were sold than nonstudents. How many of each type of ticket were sold?
This is a "solve the system" type of problem where you need TWO equations.
Let's call the student tickets: S
Let's call the NON student tickets: N
You are told that S tickets are $6 and N tickets are $9.
Therefore, this equation works:
6S + 9N = $10,500
It makes sense, don't you think that the cost of the ticket is multiplied by the number of students who attend?
We need a 2nd equation tho and that comes from this info: 250 more students tickets were sold than nonstudents.
To put it another way: S = 250 + N
Do you see how this equation can represent that student tickets represented 250 MORE tickets than the non students?
Now put the two equations together and solve:
6S + 9N = $10,500
S = 250 + N <----you know what "S" equals, so let's plug that into the first equation.
6S + 9N = $10,500 First equation
6(250 + N) + 9N = 10,500 (See how we plugged (250 + N) into the "S" variable?)
1500 + 6N + 9N = 10,500 (Distributed the 6 to the 1500 and 6 to the N)
1500 + 15N = 10,500 (Combined like terms: 6N + 9N = 15N)
15N = 9000 (Subtracted 1500 from both sides to isolate the N)
N = 600 (Divided both sides by 15 to completely isolate the N)
Now we know that 600 non student tickets were sold.
Add 250 to the NON student tickets and we have 850 student tickets. OR.. just plug it into the 2nd equation:
S = N + 250
S = 600 + 250
S = 850
Does this check out?
Let's see:
Student tickets are $6
NON student tickets are $9
Total tickets sold: $10,500
6S + 9N = 10,500
6(850) + 9(600) = 10,500
5100 + 5400 = 10,500
10,500 = 10,500
YAY it works. I hope this helps you.
|
|
|
