Step 1: Define variables and expressions

• $b$: The number of boxes Tim must sell each month.
• The total cost to produce and ship one box is the sum of the production and shipping costs: $12.35 + 2.65 = 15 \, \text{(dollars per box)}$
• The total expense for producing and shipping $b$ boxes is $15b$.
• Tim also spends $600 a month on online advertising, so his total monthly expenses are: $15b + 600$
• Tim charges $35 per box, so the total revenue from selling $b$ boxes is: $35b$

Step 2: Set up the equation

To find the number of boxes $b$ that Tim must sell for his sales to equal his monthly expenses, we set the revenue equal to the expenses: $35b = 15b + 600$

Step 3: Solve the equation

1. Subtract $15b$ from both sides: $35b - 15b = 600$ $20b = 600$

2. Divide both sides by 20: $b = \frac{600}{20} = 30$

Answer:

Tim must sell 30 boxes each month for his sales to equal his monthly expenses.

Would you like a detailed explanation of each step, or do you have any further questions?

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Relative Questions:

1. How would Tim's expenses change if the cost of shipping increased?
2. What happens to the number of boxes Tim must sell if he raises the price per box?
3. How would reducing the advertising budget affect the breakeven point?
4. What if Tim adds another fixed monthly cost? How would that affect the equation?
5. If Tim sells more than 30 boxes, how much profit will he make per box?

Tip: When solving equations, always double-check that each term (like production costs or revenue) is accounted for correctly in the equation.