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.
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Jasmine's initial cost for woodworking tools: \[ \text{Tools cost} = 286 \text{ dollars} \]
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The cost of wood per birdhouse is $12. If she sells \( x \) birdhouses, the total cost of the wood will be: \[ \text{Cost of wood} = 12x \text{ dollars} \]
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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:
- 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 \( \boxed{22} \) birdhouses in order for her sales to equal the total cost of the wood and tools.