Q10. - Algebra 1

Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

At a family fun centre, the Wilson and Sanchez families each bought video game tokens and batting cage tokens as shown in the table.

Family	Wilson	Sanchez
Number of Video Game Tokens	25	30
Number of Batting Cage Tokens	8	6
Total Cost	$\mathrm{\backslash (}26.50$	$\mathrm{\backslash )}25.50$

What is the cost in dollars of a batting cage token at the family fun centre?

Step-by-Step Solution

Answer

The cost in dollars of a batting cage token at the family fun centre is $1.75$.

Step 1. Write the system of equations for the given problem.

Let $x$ be the cost in dollars for a Video Game token.

 

Let $y$ be the cost in dollars for a Batting Cage token.

 

The system of equations for the given problem is:

$\begin{array}{l}25x+8y=26.50\left(1\right)\\ 30x+6y=25.50\left(2\right)\end{array}$

Step 2. Solve the system of equations.

Multiply the both sides of the equation (1) by 3.

$$\begin{gathered} 3\left(25x+8y\right)=3\left(26.50\right) \\ 75x+24y=79.50\left(3\right) \end{gathered}$$

Multiply the both sides of the equation (2) by 4.

$$\begin{gathered} 4\left(30x+6y\right)=4\left(25.50\right) \\ 120x+24y=102\left(4\right) \end{gathered}$$

Subtract the equation (3) from the equation (4) to eliminate the variable $y$.

$$\begin{gathered} 120x+24y-\left(75x+24y\right)=102-79.50 \\ 120x+24y-75x-24y=22.5 \\ 120x-75x=22.5 \\ 45x=22.5 \\ x=\frac{22.5}{45} \\ x=\frac{1}{2} \\ x=0.5 \end{gathered}$$

Now substitute the value of $x$ in the equation (1) to find the value of $y$.

$$\begin{gathered} 25x+8y=26.50 \\ \text{25}\left(0.5\right)+8y=26.50 \\ 12.5+8y=26.50 \\ 8y=26.50-12.5 \\ 8y=14 \\ y=\frac{14}{8} \\ y=1.75 \end{gathered}$$

The values of $x$ and $y$ are $0.5$ and $1.75$ respectively.

 

Therefore, the cost in dollars for a batting cage token is $1.75$.