Chapter 8.3, Problem 25PPS

To determine

To calculate: To find three solutions of $3x+y=12$ to find the number of regular rides $x$ and children’s rides $y$ a family can go with $12$ rides

Answer to Problem 25PPS

The solutions are $\left(4,0\right),\left(1,9\right),\left(2,6\right)$

Explanation of Solution

Given information: Regular rides cost $3$ tickets and children’s rides cost $1$ ticket

Calculation:

Given that Regular rides cost $3$ tickets and children’s rides cost $1$ ticket

Also, total number of rides for a family is $12$

Thus, equation is given as

  $3x+y=12$

Finding the two solution of the above equation:

When $y=0$

  $\begin{array}{l}3x+0=12\\ x=\frac{12}{3}\\ x=4\end{array}$

Here, $4$ regular rides and no children’s rides for a family

When $y=9$

  $\begin{array}{l}3x+9=12\\ x=\frac{3}{3}\\ x=1\end{array}$

Here, $1$ regular rides and $9$ children’s rides for a family

When $y=6$

  $\begin{array}{l}3x+6=12\\ x=\frac{6}{3}\\ x=2\end{array}$

Here, $2$ regular rides and $6$ children’s rides for a family

Conclusion:

Hence, solutions are $\left(4,0\right),\left(1,9\right),\left(2,6\right)$