SOLUTION: For a particular​ event, 916 tickets were sold for a total of ​$4538. If students paid ​$4 per ticket and nonstudents paid ​$6 per​ ticket, how many student tickets wereâ

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Question 1150640: For a particular​ event, 916 tickets were sold for a total of ​$4538. If students paid ​$4 per ticket and nonstudents paid ​$6 per​ ticket, how many student tickets were​ sold?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

    4x + 6*(916-x) = 4538,


where x is the number of student tickets.


Simplify and solve for x.


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = number of student tickets sold at 4 dollars each.
y = number of non-student tickets sold at 6 dollars each.

equations are:

x + y = 916
4x + 6yh = 4538

multiply both sides of the first equation by 4 and leave the second equation as is to get:

4x + 4y = 3664
4x + 6y = 4538

subtract the first equation from the second equation to get:

2y = 874

solve for y to get:

y = 437

since x + y = 916, then x = 479

the result is:

x + y = 479 + 437 = 916, confirming the value of x and y are solutions for the first equation.

4x + 6y = 4*479 + 6*437 = 4538, confirming the value of x and y are solutions for the second equation.

your solution is that 479 student tickets were sold.