Jasmine plans to make and sell birdhouses this summer to earn extra money. She bought some woodworking tools for $286, and she will need to buy $12 worth of wood for each birdhouse. She plans to sell the birdhouses for $25 each.

Question

How many birdhouses must Jasmine sell so that her sales equal the cost of the wood and tools?

Answer 1

To determine how many birdhouses Jasmine must sell for her sales to equal the cost of the wood and tools, we first need to calculate her total costs.

1. Jasmine's initial cost for woodworking tools: $$\text{Tools cost}=286\text{ dollars}$$

2. The cost of wood per birdhouse is $12. If she sells $x$ birdhouses, the total cost of the wood will be: $$\text{Cost of wood}=12x\text{ dollars}$$

3. Therefore, the total cost including the tools and the wood will be: $$\text{Total cost}=286+12x$$

Next, we calculate her total sales from selling $x$ birdhouses:

4. If Jasmine sells each birdhouse for $25, her total sales when she sells $x$ birdhouses will be: $$\text{Sales}=25x\text{ dollars}$$

Now, we want to find out when her total sales equal her total costs. Thus, we set up the equation: $$25x=286+12x$$

To solve for $x$, first, we can subtract $12x$ from both sides: $$25x-12x=286$$ $$13x=286$$

Next, we divide both sides by 13 to solve for $x$: $$x=\frac{286}{13}=22$$

So, Jasmine must sell $\boxed{{\displaystyle 22}}$ birdhouses in order for her sales to equal the total cost of the wood and tools.