Xavier spent 84$ on art supplies. The canvas for each of his paintings is an additional 1$. He plans to sell his paintings for 8$.Write an equation that could be used to find the number of paintings (p) he will need to sell to break even,solve the equation you make as well

Let's break down the problem step by step.

### Step 1: Define the variables
- Let $ p $ be the number of paintings Xavier needs to sell to break even.

### Step 2: Set up the equation
- **Cost:** Xavier initially spent 84 dollars on art supplies, plus 1 dollar per painting for the canvas. Therefore, the total cost for $ p $ paintings is:
  \[
  \text{Total Cost} = 84 + 1p
  \]
- **Revenue:** Xavier plans to sell each painting for 8 dollars, so his total revenue from selling $ p $ paintings will be:
  \[
  \text{Total Revenue} = 8p
  \]
  
### Step 3: Write the equation
To break even, the total revenue must equal the total cost:
\[
8p = 84 + 1p
\]

### Step 4: Solve the equation
Subtract $ 1p $ from both sides to get:
\[
8p - 1p = 84
\]
\[
7p = 84
\]
Divide both sides by 7:
\[
p = \frac{84}{7} = 12
\]

### Conclusion
Xavier needs to sell **12 paintings** to break even.

Would you like more details or have any questions?

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Here are 5 related questions you might find interesting:
1. How much profit will Xavier make if he sells 15 paintings?
2. What would happen to the break-even point if the canvas cost increased to 2 dollars per painting?
3. How much revenue does Xavier generate if he sells 20 paintings?
4. If Xavier decides to sell his paintings for 10 dollars each, how many would he need to sell to break even?
5. What is the cost function if Xavier buys additional art supplies for 50 dollars?

**Tip:** In break-even problems, always ensure to equate the total cost and total revenue to find the solution.

Learn how to calculate the break-even point for Xavier, who spent $84 on art supplies and plans to sell paintings for $8 each. Find out how many paintings he needs to sell to cover his costs. Suitable for Grades 7-9.

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