Adult tickets for a play cost $19 and child tickets cost $17. If there were 36 people at a performance and the theatre collected $646 from ticket sales, how many children attended the play?
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To solve this problem, we can set up a system of equations. Let's use two variables:
Let's call the number of adult tickets sold "a" and the number of child tickets sold "c".
From the information given, we know the following:
1) The total number of people who attended the play is 36. So, a + c = 36. (Equation 1)
2) The theatre collected a total of $646 from ticket sales. The cost of each adult ticket is $19, so the total revenue from adult tickets is 19a. Similarly, the cost of each child ticket is $17, so the total revenue from child tickets is 17c. Therefore, we can write the equation: 19a + 17c = 646. (Equation 2)
Now, we can solve this system of equations to find the values of "a" and "c".
First, we'll solve Equation 1 for "a":
a = 36 - c
Now, substitute this value for "a" in Equation 2:
19(36 - c) + 17c = 646
Expand and simplify:
684 - 19c + 17c = 646
-2c = 646 - 684
-2c = -38
c = -38 / -2
c = 19
Therefore, the number of children who attended the play is 19.