Chapter 9, Problem 44CR

To determine

To write and solve the system of equations.

Answer to Problem 44CR

The system of equations is written as:

  $\begin{array}{l}\text{3x}+\text{8y}=22\\ \text{x}+\text{y}=4\end{array}$

The solution for the system of equations is $\left(2,2\right)$ .

In the group of four people $2$ children and $2$ adults went to the museum.

Explanation of Solution

Given information:

The given statement is:

“Tickets to a museum cost $\$3$ for children and $\$8$ for adults. A group of four visitors to the museum spent a total of $\$22$ on tickets. Write and solve a system of equations to represent this situation. Interpret the solution.”

Calculation :

Let the number of children be $\text{x}$ and number of adults be $\text{y}$ .

The system of equations is written as:

  $\begin{array}{l}\text{3x}+\text{8y}=22\\ \text{x}+\text{y}=4\end{array}$

Find the value of $\text{y}$ in terms of $\text{x}$ from the second equation:

  $\begin{array}{l}\text{x}+\text{y}=4\\ \text{y}=-\text{x}+4\left[\text{Subtracting both sides by x}\right]\end{array}$

Substitute the value of $\text{y}=-\text{x}+4$ in the first equation:

  $\begin{array}{l}\text{3x}+\text{8y}=22\\ \text{3x}+\text{8}\left(-\text{x}+4\right)=22\\ 3\text{x}-8\text{x}+32=22\\ -5\text{x}=22-32\\ \text{x}=\frac{-10}{-5}\\ \text{x}=2\end{array}$

Calculate the value of $\text{y}$ substituting the value of $\text{x}$ :

  $\begin{array}{l}\text{y}=-\text{x}+4\\ \text{y}=-2+4\\ \text{y}=2\end{array}$

Hence, the solution for the system of equations is $\left(2,2\right)$ .

In the group of four people $2$ children and $2$ adults went to the museum.