Question

A new online store charges all customers one price to download any song and another price to download any game. Jenna paid $20.50 to download eight songs and three games, and Dwayne paid $22.50 to download four songs and five games. How much does the store charge to download each song and game? Use x to represent the cost of each song and y to represent the cost of each game.

Answer 1

Aright. Let's write this problem as a series of equations before turning it into matrix form. Call x the variable for the cost per song. Call y the variable for the cost per game.

Jenna then paid:
\[8x + 3y = $20.50\]

Dwayne paid:
\[4x + 5y = $22.50\]

These two represent the entire system of equations needed for this problem.

The vector for representing the fixed price per song/game can be presented as:
\[\left(\begin{matrix}x \\ y\end{matrix}\right)\]

The entire system of equations can be represented by:
\[\left[\begin{matrix}8 & 3 \\ 4 & 5\end{matrix}\right]\left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\begin{matrix}$20.50 \\ $22.50\end{matrix}\right)\]

Now, you can solve this using regular linear algebra techniques. Let me know if you need help. Also, let me know if you get an answer so that I can confirm it.