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

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Jasmine must sell 22 birdhouses to cover her costs. To determine how many birdhouses Jasmine must sell so that her sales equal the cost of the wood and tools, we can set up an equation based on her costs and revenues. 1. **Calculate the total fixed costs**: - The cost of the woodworking tools is $$ \$286 $$. - The cost of wood for each birdhouse is $$ \$12 $$. 2. **Let $$ x $$ be the number of birdhouses Jasmine sells**. The total cost for the wood for $$ x $$ birdhouses is: $$ 12x $$ 3. **Total costs** (fixed costs + variable costs): $$ \text{Total Costs} = 286 + 12x $$ 4. **Revenue from selling $$ x $$ birdhouses**: - Each birdhouse sells for $$ \$25 $$, so the total revenue is: $$ 25x $$ 5. **Set the total revenue equal to the total costs**: $$ 25x = 286 + 12x $$ 6. **Solve for $$ x $$**: - Subtract $$ 12x $$ from both sides: $$ 25x - 12x = 286 $$ $$ 13x = 286 $$ - Divide both sides by $$ 13 $$: $$ x = \frac{286}{13} \approx 22 $$ Thus, Jasmine must sell **22 birdhouses** to cover her costs.

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