\( \mathbf{8 \& 9 ) \text { Mrs. Korth is the AVID site coordinator responsible for planning the End of Year }} \) Celebration. Plans include hiring a catering service and firework display. She wants to keep the ticket price as low as possible while still covering the cost of the food and the show. 8) a) Firework Company A charges \( \$ 375 \) for a show. Firework Company B charges \( \$ 225 \) plus \( \$ 10 \) per firework lit. Write a system of equations to represent the costs of the two companies. \( A(x)= \) \( B(x)= \)

To represent the costs of the two firework companies, we can define the equations based on the information provided. 1. **Firework Company A** charges a flat fee of \( \$375 \). Therefore, the cost function for Company A can be represented as: \[ A(x) = 375 \] where \( A(x) \) is the total cost from Company A, and \( x \) does not affect the cost since it is a fixed price. 2. **Firework Company B** charges a base fee of \( \$225 \) plus \( \$10 \) for each firework lit. Thus, the cost function for Company B can be represented as: \[ B(x) = 225 + 10x \] where \( B(x) \) is the total cost from Company B, and \( x \) represents the number of fireworks lit. Now we have the system of equations representing the costs of the two companies: \[ \begin{align*} A(x) & = 375 \\ B(x) & = 225 + 10x \end{align*} \]