Chapter 9.7, Problem 24HP

To determine

To write : a real-world problem that can be solved by a system of equations.

To solve and interpret the solution of the system of equations.

Answer to Problem 24HP

Consider a family of fifteen members goes to a water park. The children are given red bands and the adults are given green bands. The green bands are twice as many as the red bands. To calculate the number of children and adults in the family.

The system of equations for the given situation:

  $\begin{array}{l}x+y=15\\ y=2x\end{array}$

The solution of this system of equations is $\text{(5},10)$ .Thus, there are $5$ children and $\text{10}$ adults in the family of $15$ .

Explanation of Solution

Given information :

A real-world problem that can be solved by a system of equations.

Calculation :

As per the question,

Consider a family of fifteen members goes to a water park. The children are given red bands and the adults are given green bands. The green bands are twice as many as the red bands. To calculate the number of children and adults in the family.

Let the number of children be $x$ and that of adultsbe $y$ .

Total number of family members is $15$ .

The green bands are twice as many as the red bands.

Therefore, the system of equations for the given situation:

  $\begin{array}{l}x+y=15\\ y=2x\end{array}$

Find the value of $x$ by substituting $2x$ for $y$ in the first equation.

  $\begin{array}{l}x+y=15\text{ [Write the first equation]}\\ x+2x=15\text{ [Substitute }y=2x\text{]}\\ \text{ 3}x=15\text{ [Combine like terms}]\\ x=5\text{ [Divide both sides by 3}]\end{array}$

Substitute $5$ for $x$ in either equation to find the value of $y$ .

  $\begin{array}{l}\text{}\text{}\text{}\text{}\text{}y=2x\text{ [Write the second equation]}\\ y=2(5)\text{ [}x=5\text{]}\\ y=10\text{ [Simplify}]\end{array}$

The solution of this system of equations is $\text{(5},10)$ .

Thus, there are $5$ children and $\text{10}$ adults in the family of $15$ .