SOLUTION: Adult tickets for a play costs $14 and child tickets costs $3. If there were 26 people at a performance and the theater collected $199 from ticket sales. How many adults and childr

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Question 107610: Adult tickets for a play costs $14 and child tickets costs $3. If there were 26 people at a performance and the theater collected $199 from ticket sales. How many adults and children attended the play?
Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
According to the given data it is given that

Let the adult be represented by x and the cost of an adult ticket is $14

Let the children be represented by y and the cost of the per ticket is $3

And the amount collected at that show is $199

Now let us form the simultaneous equations and then solve them.

The equations are:

14x + 3y = 199 ---------------(1)
x + y = 26 ---------------(2)
=============================
Multiply EQN (2) by 3 and subtract it from (1)


14x + 3y = 199

3x + 3y = 78
- - -
===============
11x = 121


==> +x+=+121%2F11

==> x = 11

by back substitution we find the value of y.

11 + y = 26

==> y = 26 - 11

==> y = 15

Hence, 15 children and 11 adults attended the show.