Chapter 6.3, Problem 23PPS

To determine

To find the adult price and the children’s price of admission for a 3D movie.

Answer to Problem 23PPS

Adult’s price: $17.95

Children’s price: $13.95

Explanation of Solution

Calculation:

Let x denote the cost of admissionfor 3D movie of adults and y denote the cost of admission for 3D movie of children. Then,

From the given table,

Cost of admission for Blackwell’s family can be represented as:

  $2x+5y=105.65\to \text{(1)}$

Cost of admission for Jones’s family can be represented as:

  $2x+3y=77.75\to \text{(2)}$

Total cost of admission for both the families is represented as:

  $4x+8y=183.4\to \text{(3)}$

Subtract (2) from (1),

  $\begin{array}{l}\text{ 2}x+5y=105.65\\ \frac{-2x-3y=-77.75}{2y=27.9}\text{ [When subtracting the sign of (2) changes]}\end{array}$

  $\begin{array}{c}2y=27.9\text{ [Dividing 2 on both sides]}\\ y=\frac{27.9}{2}\\ y=13.95\end{array}$

Substitute the value of $y=13.95$ in any one of the equations.

Say, equation (2),

  $\begin{array}{c}2x+3(13.95)=77.75\\ 2x+41.85=77.75\text{ [Subtracting 41}\text{.85 on both sides]}\\ 2x=77.75-41.85\\ 2x=35.9\\ x=\frac{35.9}{2}\text{ [Dividing 2 on both sides]}\\ x=17.95\end{array}$

Conclusion:

Therefore, the cost of admission for 3D movie for adults is $17.95 and children is $13.95