Sure! Let's solve this step by step using a system of equations and the method of elimination.

Problem Breakdown:

• The store's fixed costs per month are $4000.
• The cost to the store per bike is $80.
• The selling price of each bike is $160.

The objective is to determine how many bicycles the store must sell to break even, meaning that the store's revenue equals its costs.

Step 1: Set up the system of equations.

Let $x$ represent the number of bicycles the store sells each month.

• Equation 1 (Costs equation): The total cost for the store includes its fixed operating costs ($4000) plus the cost per bike ($80) multiplied by the number of bikes sold ($x$). $\text{Total Costs} = 4000 + 80x$

• Equation 2 (Revenue equation): The total revenue for the store comes from selling bikes at $160 each. The revenue is therefore: $\text{Total Revenue} = 160x$

At the break-even point, the store’s revenue equals its costs, so: $4000 + 80x = 160x$

Next Step:

Now, we have the system of equations:

1. & \quad 4000 + 80x = 160x \\ \end{aligned}$$ In the next step, we'll solve for $$x$$ by eliminating terms and solving the equation. Let me know if you'd like to proceed with that! Would you like to go further and solve for $$x$$? Or do you have any questions about this first step? --- Here are some related questions to consider: 1. How do you solve an equation for a variable? 2. What does the "break-even point" mean in business terms? 3. How does the concept of fixed costs versus variable costs affect business operations? 4. Can you calculate the store's profit if it sells more than the break-even number of bikes? 5. What happens if the cost per bike increases? How would that affect the break-even point? **Tip**: When solving for $$x$$ in an equation, always aim to isolate the variable on one side by using inverse operations, like subtraction or division!