Chapter 8, Problem 10STP

To determine

The number of the adult tickets did the Mr. Branson purchase.

Answer to Problem 10STP

The number of the adult ticket is 4.

Explanation of Solution

Given:

Mr. Branson bought the total of 9 tickets to the zoo. He bought children tickets at the rate of the $6.50 and the adult tickets for $9.25 each. He spend $69.50 altogether.

Considering the number of the children’s ticket is x.

The number of the adult ticket is y.

Hence, the equation will be:

  $\begin{array}{l}x+y=9\\ y=9-x\mathrm{........}\left(1\right)\end{array}$

And the expression for the total expenses:

  $6.50x+9.25y=69.50\mathrm{........}\left(2\right)$

Substituting the value of the y in the equation 2:

  $\begin{array}{c}6.50x+9.25\left(9-x\right)=69.50\\ 6.50x+83.25-9.25x=69.50\\ -2.75x=69.50-83.25\\ -2.75x=-13.75\\ x=\frac{13.75}{2.75}\\ x=5\end{array}$

Now, substituting the value of the x into the equation 1:

  $\begin{array}{l}y=9-x\\ y=9-5\\ y=4\end{array}$

Therefore, the number of the adult ticket is 4.