Chapter 6.8, Problem 60SR

To determine

the number of each type of tickets.

Answer to Problem 60SR

The number of adult tickets is: $8$

Again, the number of children tickets is: $3$

Explanation of Solution

Given:

  $11$ Members tickets

total cost i $\$156$ .

  

Calculation:

Assume the number of adult tickets is: $x$

Again, the number of children tickets is: $y$

Here the two equations would be:

  $x+y=\mathrm{11........}(1)$

And,

  $15x+12y=\mathrm{156......}(2)$

The strategy is to find the number of each type of tickets.

From equation $(1)$ ,

  $\begin{array}{l}x+y=11\\ x+y-x=11-x\\ y=11-x\mathrm{.......}(3)\end{array}$

Now, substituting the value of $y$ in equation $(2)$ ,

  $\begin{array}{l}15x+12\left(11-x\right)=156\\ 15x+132-12x=156\\ 3x=156-132\\ \frac{3x}{3}=\frac{24}{3} [Divide both sides by3]\\ x=8\end{array}$

Again, form $(3),$

  $\begin{array}{l}y=11-8\\ =3\end{array}$

Hence, the number of adult tickets is: $8$

Again, the number of children tickets is: $3$

Conclusion:

Hence, the number of adult tickets is: $8$

Again, the number of children tickets is: $3$