Questions: A team wants to create custom reusable water bottles. The team members need to compare the cost between two companies to make them. Waterworks charges 50 for a setup fee and 5 per bottle. Bottlemania charges 14 for a setup fee and 8 per bottle. Here is a graph that represents the costs at each company.

A team wants to create custom reusable water bottles. The team members need to compare the cost between two companies to make them.

Waterworks charges 50 for a setup fee and 5 per bottle.
Bottlemania charges 14 for a setup fee and 8 per bottle.
Here is a graph that represents the costs at each company.

Transcript text: A team wants to create custom reusable water bottles. The team members need to compare the cost between two companies to make them. Waterworks charges $\$ 50$ for a setup fee and $\$ 5$ per bottle. Bottlemania charges $\$ 14$ for a setup fee and $\$ 8$ per bottle. Here is a graph that represents the costs at each company.

Solution

Solution Steps

Step 1: Define the cost functions for both companies

Waterworks: Setup fee is $50, and the cost per bottle is $5.
- Cost function: $ C_W = 50 + 5x $
Bottlemania: Setup fee is $14, and the cost per bottle is $8.
- Cost function: $ C_B = 14 + 8x $

Step 2: Set up the equation to find the break-even point