Chapter 6.2, Problem 23PPE

To determine

To calculate: Number of children and adults in a group.

Answer to Problem 23PPE

Total number of children $=2$

Total number of adults $=9$

Explanation of Solution

Given information: Adult tickets to a play cost $\$22$ . Tickets for children cost $\$15$ . Tickets for a group of 11 people cost a total of $\$228$ .

Calculation:

Let $x$ denotes number of children and $y$ denotes number of adults in a group.

Total number of people $=11$

So,

  $x+y=11(i)$

Total cost of tickets of children $=15x$

Total cost of tickets of adults $=22y$

Total amount of tickets of people in a group $=\$228$

So,

  $15x+22y=228(ii)$

From $(i)$ , put $x=11-y$ in $15x+22y=228$

  $\begin{array}{l}15\left(11-y\right)+22y=228\\ \Rightarrow 165-15y+22y=228\\ \Rightarrow 165+7y=228\\ \Rightarrow 7y=228-165\\ \Rightarrow 7y=63\\ \Rightarrow y=9\end{array}$

Put $y=9$ in $x=11-y$

  $x=11-9=2$

Therefore,

Total number of children $=2$ .

Total number of adults $=9$ .