Question

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?
birdhouses

Answer 1

To determine how many birdhouses Jasmine needs to sell to cover her costs, we first need to set up an equation based on her expenses and income.

**Costs:**
- Initial tool cost: $286
- Wood cost per birdhouse: $12

Let's denote the number of birdhouses Jasmine sells as \( x \). Then, her total costs for \( x \) birdhouses can be expressed as:
\[
\text{Total Cost} = 286 + 12x
\]

**Income:**
- Selling price per birdhouse: $25

The income from selling \( x \) birdhouses can be expressed as:
\[
\text{Total Income} = 25x
\]

We want her total income to equal her total costs:
\[
25x = 286 + 12x
\]

Now, let's solve for \( x \):

1. Subtract \( 12x \) from both sides:
\[
25x - 12x = 286
\]
\[
13x = 286
\]

2. Divide both sides by 13:
\[
x = \frac{286}{13}
\]
\[
x = 22
\]

Jasmine must sell **22 birdhouses** to cover the costs of her tools and wood.