Question 74620: Adult tickets for a play cost $9 and child tickets cost $8. If there were 23 people at a performance and the theater collected $193 from ticket sales, how many children attended the play?
Answer by rvaught(1)   (Show Source):
You can put this solution on YOUR website! What you want to do here is to solve a system of equations by setting up two linear equations, with your x and y variables aligned on the same side. Let x represent adult tickets, and y represent child tickets. Then,
x + y = 23 (means that the number of 'x' tickets plus the number of 'y' tickets total 23).
Also, 9x+8y=193 (means that the number of x tickets, times the cost of $9 each, plus the number of y tickets, times the cost of $8 each, totalled $193).
Now, line the two equations up with one above the other, and use one of the methods for solving systems of equations:
x+y=23
9x+8y=193
Substitution would probably be your best bet here, since the first equation has variables with coefficients of 1. So, solve for one of the variables. If x+y=23, then subtract y from both sides to get x=23-y. Plug this value into the second equation: 9(23-y)+8y=193. Now, you only have one variable, which can be solved for. Find the value of y. First, distribute the 9. Then,
9(23-y)+8y=193
(9*23)-(9*y)+8y=193
207-9y+8y=193
207-y=193
y=14
This tells us that 14 'child' tickets were sold. We can plug this value into the first equation to find that if 14 'child' tickets were sold, and a total of 23 tickets were sold, then 9 'adult' tickets were sold (23-14=9).
Going back to the question, it asks for the number of children that attended. We found that 14 'child' tickets were sold.
Hope this helps!
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