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?

Question

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?

Answer 1

A. Using algebra

Let
A=number of adults who attended, then
36-A = number of children who attended
19A + 17(36-A) = 646
Solve for A.

B. Using arithmetic
If only adults went, ticket sales would have collected 36*19=$684
For every child who went, sales would reduce by $2.
So number of children=(684-646)/2=19

Answer 2

Let's say the number of adult tickets sold is A.

And the number of child tickets sold is C.

According to the given information, the total number of people who attended the play is 36:
A + C = 36 --------(1)

The cost of one adult ticket is $19, so the total revenue from adult tickets can be calculated as follows:
19A

Similarly, the cost of one child ticket is $17, so the total revenue from child tickets is:
17C

According to the given information, the total revenue from ticket sales is $646:
19A + 17C = 646 --------(2)

Now, we can solve these two equations to find the value of C.

First, let's rearrange equation (1) to express A in terms of C:
A = 36 - C

Substitute this expression for A in equation (2), and solve for C:
19(36 - C) + 17C = 646
684 - 19C + 17C = 646
-2C = 646 - 684
-2C = -38
C = -38 / -2
C = 19

Therefore, there were 19 children who attended the play.

Answer 3

To find the number of children who attended the play, we first need to determine the number of adult tickets sold.

Let's assume that the number of adult tickets sold is x.

Since each adult ticket costs $19, the revenue from adult tickets can be represented as 19x.

Since the total number of people at the play was 36, the number of children can be represented as (36 - x).

Each child ticket costs $17, so the revenue from child tickets can be represented as 17(36 - x).

According to the problem, the theater collected a total of $646 from ticket sales. This can be represented as:

19x + 17(36 - x) = 646

Now, we can solve for x to find the number of adult tickets sold:

19x + 612 - 17x = 646

2x = 646 - 612

2x = 34

x = 34 / 2

x = 17

So, 17 adult tickets were sold. Now, let's find the number of children who attended the play:

Number of children = 36 - x
Number of children = 36 - 17
Number of children = 19

Therefore, 19 children attended the play.